pivot_wider_indices <- function(data) {
data |>
add_count(user_id, game_name) |>
mutate(
game_index = if_else(
n == 1,
game_name,
str_c(game_name, index_name, sep = "-")
)
) |>
pivot_wider(
id_cols = user_id,
names_from = game_index,
values_from = test
)
}targets::tar_load(users, store = here::here("preproc/_targets"))
ind_filt <- readxl::read_excel(here::here("config/indices_filtering.xlsx"))
dim_order <- c("attention", "multitask", "switching", "inhibition",
"reasoning", "complex span", "working memory", "short term memory",
"long term memory", "probability learning",
"speeded IP", "strategic IP",
"perception", "math", "language")
indices_clean <- targets::tar_read(indices_clean, store = here::here("preproc/_targets")) |>
full_join(ind_filt, by = c("game_name", "index_name")) |>
anti_join(
filter(users, grade == "20220303级"),
by = "user_id"
) |>
filter(
!is.na(check_result) & check_result != "target-stash",
!game_name %in% c("文字推理", "数字推理")
) |>
arrange(factor(dimension, dim_order)) |>
mutate(test = if_else(reversed, -test, test)) |>
group_by(game_name, index_name) |>
mutate(test = if_else(test %in% boxplot.stats(test)$out, NA_real_, test)) |>
ungroup()
indices_memory <- indices_clean |>
filter(
dimension %in% c("complex span", "working memory", "short term memory"),
!game_name %in% c("魔术师终极", "人工语言-中级", "欢乐餐厅", "过目不忘PRO", "连续再认")
)The include tasks:
indices_memory |>
pivot_wider_indices() |>
select(-user_id) |>
correlate(quiet = TRUE) |>
rearrange(method = "HC") |>
stretch() |>
mutate(across(c(x, y), as_factor)) |>
ggplot(aes(x, y)) +
geom_tile(aes(fill = r)) +
scico::scale_fill_scico(palette = "bam", midpoint = 0, direction = -1) +
coord_fixed() +
theme_minimal(base_size = 18) +
labs(x = "", y = "", fill = "Pearson's", color = "") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))All span tasks use
mean_span_pcuindex, and all n-back tasks usedprimeindex.
indices_memory <- indices_clean |>
filter(
dimension %in% c("complex span", "working memory", "short term memory"),
!game_name %in% c("魔术师终极", "人工语言-中级", "欢乐餐厅", "过目不忘PRO", "连续再认")
)
indices_selected <- indices_memory |>
filter(index_name %in% c("mean_span_pcu", "dprime")) |>
pivot_wider_indices() |>
select(-user_id)correlate(indices_selected, quiet = TRUE) |>
rearrange(method = "HC") |>
stretch() |>
mutate(across(c(x, y), as_factor)) |>
ggplot(aes(x, y)) +
geom_tile(aes(fill = r)) +
scico::scale_fill_scico(palette = "bam", midpoint = 0, direction = -1) +
coord_fixed() +
theme_minimal(base_size = 18) +
labs(x = "", y = "", fill = "Pearson's", color = "") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
mds <- indices_selected |>
cor(use = "pairwise") |>
smacof::sim2diss(to.dist = TRUE) |>
smacof::mds(ndim = 2, type = "mspline")Registered S3 methods overwritten by 'proxy':
method from
print.registry_field registry
print.registry_entry registryplot(mds)
nfactors_test <- psych::nfactors(indices_selected)Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
ultra-Heywood case was detected. Examine the results carefully
fit <- psych::fa(indices_selected, 3)Loading required namespace: GPArotationpsych::fa.diagram(fit)
fit_bifac <- psych::omega(indices_selected, 3, plot = FALSE)
psych::omega.diagram(fit_bifac)
mcmc <- indices_selected |>
mutate(across(.fns = ~ scale(.)[, 1])) |>
befa(verbose = FALSE) |>
post.column.switch() |>
post.sign.switch()hppm <- summary(mcmc, what = "hppm")
hppm |>
pluck("alpha", "m1") |>
as_tibble(rownames = "alpha_term") |>
separate(alpha_term, c(NA, "game_index"), sep = ":") |>
mutate(game_index = reorder(game_index, dedic)) |>
ggplot(aes(game_index, dedic)) +
geom_tile(aes(fill = mean)) +
geom_text(aes(label = round(mean, 2)), color = "white") +
scico::scale_fill_scico(palette = "bam", midpoint = 0, direction = -1) +
coord_fixed() +
theme_minimal(base_size = 18) +
labs(x = "Term", y = "Factor",
title = str_c("Posterior Probability: ", round(hppm$hppm$prob, 2),
", with ", hppm$hppm$nfac, " factors")) +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
Firstly, the model from EFA is tested.
fitted1 <- lavaan::cfa(
'Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted1, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 15 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 36
Number of observations 469
Number of missing patterns 55
Model Test User Model:
Standard Robust
Test Statistic 115.266 114.149
Degrees of freedom 41 41
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.010
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1347.235 1273.996
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.057
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.943 0.940
Tucker-Lewis Index (TLI) 0.923 0.920
Robust Comparative Fit Index (CFI) 0.943
Robust Tucker-Lewis Index (TLI) 0.923
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6185.158 -6185.158
Scaling correction factor 1.041
for the MLR correction
Loglikelihood unrestricted model (H1) -6127.525 -6127.525
Scaling correction factor 1.024
for the MLR correction
Akaike (AIC) 12442.315 12442.315
Bayesian (BIC) 12591.737 12591.737
Sample-size adjusted Bayesian (BIC) 12477.480 12477.480
Root Mean Square Error of Approximation:
RMSEA 0.062 0.062
90 Percent confidence interval - lower 0.049 0.048
90 Percent confidence interval - upper 0.076 0.075
P-value RMSEA <= 0.05 0.065 0.072
Robust RMSEA 0.062
90 Percent confidence interval - lower 0.049
90 Percent confidence interval - upper 0.076
Standardized Root Mean Square Residual:
SRMR 0.037 0.037fitted1_alt <- lavaan::cfa(
'Updating1 =~ `美术卡片` + `数字卡片`
Updating2 =~ `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_alt, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted1_alt, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 20 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 39
Number of observations 469
Number of missing patterns 55
Model Test User Model:
Standard Robust
Test Statistic 64.777 63.925
Degrees of freedom 38 38
P-value (Chi-square) 0.004 0.005
Scaling correction factor 1.013
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1347.235 1273.996
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.057
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.979 0.979
Tucker-Lewis Index (TLI) 0.970 0.969
Robust Comparative Fit Index (CFI) 0.980
Robust Tucker-Lewis Index (TLI) 0.971
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6159.913 -6159.913
Scaling correction factor 1.035
for the MLR correction
Loglikelihood unrestricted model (H1) -6127.525 -6127.525
Scaling correction factor 1.024
for the MLR correction
Akaike (AIC) 12397.826 12397.826
Bayesian (BIC) 12559.700 12559.700
Sample-size adjusted Bayesian (BIC) 12435.922 12435.922
Root Mean Square Error of Approximation:
RMSEA 0.039 0.038
90 Percent confidence interval - lower 0.022 0.021
90 Percent confidence interval - upper 0.055 0.054
P-value RMSEA <= 0.05 0.872 0.886
Robust RMSEA 0.038
90 Percent confidence interval - lower 0.021
90 Percent confidence interval - upper 0.054
Standardized Root Mean Square Residual:
SRMR 0.031 0.031fitted1_alt2 <- lavaan::cfa(
'Updating =~ Updating1 + Updating2
Updating1 =~ `美术卡片` + `数字卡片`
Updating2 =~ `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_alt2, what = "std", edge.color = "black",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted1_alt2, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 32 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 38
Number of observations 469
Number of missing patterns 55
Model Test User Model:
Standard Robust
Test Statistic 64.918 64.130
Degrees of freedom 39 39
P-value (Chi-square) 0.006 0.007
Scaling correction factor 1.012
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1347.235 1273.996
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.057
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.980 0.979
Tucker-Lewis Index (TLI) 0.972 0.971
Robust Comparative Fit Index (CFI) 0.980
Robust Tucker-Lewis Index (TLI) 0.972
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6159.984 -6159.984
Scaling correction factor 1.037
for the MLR correction
Loglikelihood unrestricted model (H1) -6127.525 -6127.525
Scaling correction factor 1.024
for the MLR correction
Akaike (AIC) 12395.967 12395.967
Bayesian (BIC) 12553.690 12553.690
Sample-size adjusted Bayesian (BIC) 12433.086 12433.086
Root Mean Square Error of Approximation:
RMSEA 0.038 0.037
90 Percent confidence interval - lower 0.020 0.020
90 Percent confidence interval - upper 0.053 0.053
P-value RMSEA <= 0.05 0.897 0.908
Robust RMSEA 0.037
90 Percent confidence interval - lower 0.020
90 Percent confidence interval - upper 0.053
Standardized Root Mean Square Residual:
SRMR 0.031 0.031fitted1_bifac <- lavaan::cfa(
'Common =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片` + `幸运小球` + `密码箱` + `顺背数PRO` + `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`
Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE, orthogonal = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_bifac, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0,
bifactor = "Common"
)
lavaan::summary(fitted1_bifac, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 45 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 44
Number of observations 469
Number of missing patterns 55
Model Test User Model:
Standard Robust
Test Statistic 68.845 74.976
Degrees of freedom 33 33
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.918
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1347.235 1273.996
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.057
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.972 0.966
Tucker-Lewis Index (TLI) 0.954 0.943
Robust Comparative Fit Index (CFI) 0.970
Robust Tucker-Lewis Index (TLI) 0.950
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6161.947 -6161.947
Scaling correction factor 1.104
for the MLR correction
Loglikelihood unrestricted model (H1) -6127.525 -6127.525
Scaling correction factor 1.024
for the MLR correction
Akaike (AIC) 12411.894 12411.894
Bayesian (BIC) 12594.521 12594.521
Sample-size adjusted Bayesian (BIC) 12454.873 12454.873
Root Mean Square Error of Approximation:
RMSEA 0.048 0.052
90 Percent confidence interval - lower 0.032 0.036
90 Percent confidence interval - upper 0.064 0.068
P-value RMSEA <= 0.05 0.553 0.393
Robust RMSEA 0.050
90 Percent confidence interval - lower 0.035
90 Percent confidence interval - upper 0.065
Standardized Root Mean Square Residual:
SRMR 0.041 0.041fitted1_higher <- lavaan::cfa(
'Common =~ Updating + VerbalSTM + SpatialSTM
Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_higher, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0,
bifactor = "Common"
)
lavaan::summary(fitted1_higher, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 35 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 36
Number of observations 469
Number of missing patterns 55
Model Test User Model:
Standard Robust
Test Statistic 115.266 114.149
Degrees of freedom 41 41
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.010
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1347.235 1273.996
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.057
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.943 0.940
Tucker-Lewis Index (TLI) 0.923 0.920
Robust Comparative Fit Index (CFI) 0.943
Robust Tucker-Lewis Index (TLI) 0.923
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6185.158 -6185.158
Scaling correction factor 1.041
for the MLR correction
Loglikelihood unrestricted model (H1) -6127.525 -6127.525
Scaling correction factor 1.024
for the MLR correction
Akaike (AIC) 12442.315 12442.315
Bayesian (BIC) 12591.737 12591.737
Sample-size adjusted Bayesian (BIC) 12477.480 12477.480
Root Mean Square Error of Approximation:
RMSEA 0.062 0.062
90 Percent confidence interval - lower 0.049 0.048
90 Percent confidence interval - upper 0.076 0.075
P-value RMSEA <= 0.05 0.065 0.072
Robust RMSEA 0.062
90 Percent confidence interval - lower 0.049
90 Percent confidence interval - upper 0.076
Standardized Root Mean Square Residual:
SRMR 0.037 0.037fitted2 <- lavaan::cfa(
'Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted2, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted2, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 15 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 33
Number of observations 469
Number of missing patterns 50
Model Test User Model:
Standard Robust
Test Statistic 97.634 97.382
Degrees of freedom 32 32
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.003
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1251.825 1191.197
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.051
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.946 0.943
Tucker-Lewis Index (TLI) 0.924 0.920
Robust Comparative Fit Index (CFI) 0.946
Robust Tucker-Lewis Index (TLI) 0.923
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5595.957 -5595.957
Scaling correction factor 1.030
for the MLR correction
Loglikelihood unrestricted model (H1) -5547.140 -5547.140
Scaling correction factor 1.017
for the MLR correction
Akaike (AIC) 11257.914 11257.914
Bayesian (BIC) 11394.884 11394.884
Sample-size adjusted Bayesian (BIC) 11290.148 11290.148
Root Mean Square Error of Approximation:
RMSEA 0.066 0.066
90 Percent confidence interval - lower 0.051 0.051
90 Percent confidence interval - upper 0.081 0.081
P-value RMSEA <= 0.05 0.037 0.038
Robust RMSEA 0.066
90 Percent confidence interval - lower 0.051
90 Percent confidence interval - upper 0.081
Standardized Root Mean Square Residual:
SRMR 0.037 0.037fitted2_alt <- lavaan::cfa(
'Updating1 =~ `美术卡片` + `数字卡片`
Updating2 =~ `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_alt, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted1_alt, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 20 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 39
Number of observations 469
Number of missing patterns 55
Model Test User Model:
Standard Robust
Test Statistic 64.777 63.925
Degrees of freedom 38 38
P-value (Chi-square) 0.004 0.005
Scaling correction factor 1.013
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1347.235 1273.996
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.057
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.979 0.979
Tucker-Lewis Index (TLI) 0.970 0.969
Robust Comparative Fit Index (CFI) 0.980
Robust Tucker-Lewis Index (TLI) 0.971
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6159.913 -6159.913
Scaling correction factor 1.035
for the MLR correction
Loglikelihood unrestricted model (H1) -6127.525 -6127.525
Scaling correction factor 1.024
for the MLR correction
Akaike (AIC) 12397.826 12397.826
Bayesian (BIC) 12559.700 12559.700
Sample-size adjusted Bayesian (BIC) 12435.922 12435.922
Root Mean Square Error of Approximation:
RMSEA 0.039 0.038
90 Percent confidence interval - lower 0.022 0.021
90 Percent confidence interval - upper 0.055 0.054
P-value RMSEA <= 0.05 0.872 0.886
Robust RMSEA 0.038
90 Percent confidence interval - lower 0.021
90 Percent confidence interval - upper 0.054
Standardized Root Mean Square Residual:
SRMR 0.031 0.031fitted2_alt2 <- lavaan::cfa(
'Updating =~ Updating1 + Updating2
Updating1 =~ `美术卡片` + `数字卡片`
Updating2 =~ `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted2_alt2, what = "std", edge.color = "black",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted2_alt2, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 33 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 35
Number of observations 469
Number of missing patterns 50
Model Test User Model:
Standard Robust
Test Statistic 47.237 46.994
Degrees of freedom 30 30
P-value (Chi-square) 0.024 0.025
Scaling correction factor 1.005
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1251.825 1191.197
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.051
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.986 0.985
Tucker-Lewis Index (TLI) 0.979 0.978
Robust Comparative Fit Index (CFI) 0.986
Robust Tucker-Lewis Index (TLI) 0.979
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5570.758 -5570.758
Scaling correction factor 1.027
for the MLR correction
Loglikelihood unrestricted model (H1) -5547.140 -5547.140
Scaling correction factor 1.017
for the MLR correction
Akaike (AIC) 11211.517 11211.517
Bayesian (BIC) 11356.788 11356.788
Sample-size adjusted Bayesian (BIC) 11245.705 11245.705
Root Mean Square Error of Approximation:
RMSEA 0.035 0.035
90 Percent confidence interval - lower 0.013 0.013
90 Percent confidence interval - upper 0.053 0.053
P-value RMSEA <= 0.05 0.906 0.911
Robust RMSEA 0.035
90 Percent confidence interval - lower 0.013
90 Percent confidence interval - upper 0.053
Standardized Root Mean Square Residual:
SRMR 0.029 0.029fitted2_bifac <- lavaan::cfa(
'Common =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片` + `幸运小球` + `密码箱` + `顺背数PRO` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`
Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE, orthogonal = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted2_bifac, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0,
bifactor = "Common"
)
lavaan::summary(fitted2_bifac, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 45 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 40
Number of observations 469
Number of missing patterns 50
Model Test User Model:
Standard Robust
Test Statistic 53.281 61.852
Degrees of freedom 25 25
P-value (Chi-square) 0.001 0.000
Scaling correction factor 0.861
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1251.825 1191.197
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.051
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.977 0.968
Tucker-Lewis Index (TLI) 0.958 0.942
Robust Comparative Fit Index (CFI) 0.974
Robust Tucker-Lewis Index (TLI) 0.953
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5573.780 -5573.780
Scaling correction factor 1.114
for the MLR correction
Loglikelihood unrestricted model (H1) -5547.140 -5547.140
Scaling correction factor 1.017
for the MLR correction
Akaike (AIC) 11227.561 11227.561
Bayesian (BIC) 11393.585 11393.585
Sample-size adjusted Bayesian (BIC) 11266.633 11266.633
Root Mean Square Error of Approximation:
RMSEA 0.049 0.056
90 Percent confidence interval - lower 0.031 0.037
90 Percent confidence interval - upper 0.067 0.075
P-value RMSEA <= 0.05 0.504 0.276
Robust RMSEA 0.052
90 Percent confidence interval - lower 0.036
90 Percent confidence interval - upper 0.069
Standardized Root Mean Square Residual:
SRMR 0.040 0.040fitted2_higher <- lavaan::cfa(
'Common =~ Updating + VerbalSTM + SpatialSTM
Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted2_higher, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0,
bifactor = "Common"
)
lavaan::summary(fitted2_higher, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 34 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 33
Number of observations 469
Number of missing patterns 50
Model Test User Model:
Standard Robust
Test Statistic 97.634 97.382
Degrees of freedom 32 32
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.003
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1251.825 1191.197
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.051
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.946 0.943
Tucker-Lewis Index (TLI) 0.924 0.920
Robust Comparative Fit Index (CFI) 0.946
Robust Tucker-Lewis Index (TLI) 0.923
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5595.957 -5595.957
Scaling correction factor 1.030
for the MLR correction
Loglikelihood unrestricted model (H1) -5547.140 -5547.140
Scaling correction factor 1.017
for the MLR correction
Akaike (AIC) 11257.914 11257.914
Bayesian (BIC) 11394.884 11394.884
Sample-size adjusted Bayesian (BIC) 11290.148 11290.148
Root Mean Square Error of Approximation:
RMSEA 0.066 0.066
90 Percent confidence interval - lower 0.051 0.051
90 Percent confidence interval - upper 0.081 0.081
P-value RMSEA <= 0.05 0.037 0.038
Robust RMSEA 0.066
90 Percent confidence interval - lower 0.051
90 Percent confidence interval - upper 0.081
Standardized Root Mean Square Residual:
SRMR 0.037 0.037The covariance estimate for latent variables is not correct. The estimated correlation between “Simple” and “Complex” is larger than 1.
fitted3 <- lavaan::cfa(
'Complex =~ `打靶场` + `蝴蝶照相机` + `幸运小球`
Nback =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
Simple =~ `密码箱` + `顺背数PRO` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
is not positive definite;
use lavInspect(fit, "cov.lv") to investigate.semPlot::semPaths(
fitted3, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted3, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 17 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 33
Number of observations 469
Number of missing patterns 50
Model Test User Model:
Standard Robust
Test Statistic 171.820 173.236
Degrees of freedom 32 32
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.992
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1251.825 1191.197
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.051
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.884 0.877
Tucker-Lewis Index (TLI) 0.837 0.827
Robust Comparative Fit Index (CFI) 0.884
Robust Tucker-Lewis Index (TLI) 0.836
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5633.050 -5633.050
Scaling correction factor 1.041
for the MLR correction
Loglikelihood unrestricted model (H1) -5547.140 -5547.140
Scaling correction factor 1.017
for the MLR correction
Akaike (AIC) 11332.100 11332.100
Bayesian (BIC) 11469.070 11469.070
Sample-size adjusted Bayesian (BIC) 11364.335 11364.335
Root Mean Square Error of Approximation:
RMSEA 0.097 0.097
90 Percent confidence interval - lower 0.083 0.083
90 Percent confidence interval - upper 0.111 0.111
P-value RMSEA <= 0.05 0.000 0.000
Robust RMSEA 0.097
90 Percent confidence interval - lower 0.083
90 Percent confidence interval - upper 0.111
Standardized Root Mean Square Residual:
SRMR 0.054 0.054Not fitted well.
fitted4 <- lavaan::cfa(
'Verbal =~ 数字卡片 + 文字卡片 + 幸运小球 + 密码箱 + 顺背数PRO
Spatial =~ 格子卡片 + 打靶场 + 蝴蝶照相机 + 位置记忆PRO
Object =~ 美术卡片 + 宇宙黑洞',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted4, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted4, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 19 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 36
Number of observations 469
Number of missing patterns 55
Model Test User Model:
Standard Robust
Test Statistic 286.789 289.021
Degrees of freedom 41 41
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.992
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1347.235 1273.996
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.057
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.810 0.797
Tucker-Lewis Index (TLI) 0.745 0.727
Robust Comparative Fit Index (CFI) 0.809
Robust Tucker-Lewis Index (TLI) 0.744
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6270.919 -6270.919
Scaling correction factor 1.061
for the MLR correction
Loglikelihood unrestricted model (H1) -6127.525 -6127.525
Scaling correction factor 1.024
for the MLR correction
Akaike (AIC) 12613.838 12613.838
Bayesian (BIC) 12763.259 12763.259
Sample-size adjusted Bayesian (BIC) 12649.003 12649.003
Root Mean Square Error of Approximation:
RMSEA 0.113 0.114
90 Percent confidence interval - lower 0.101 0.101
90 Percent confidence interval - upper 0.126 0.126
P-value RMSEA <= 0.05 0.000 0.000
Robust RMSEA 0.113
90 Percent confidence interval - lower 0.101
90 Percent confidence interval - upper 0.126
Standardized Root Mean Square Residual:
SRMR 0.066 0.066All span tasks use
mean_span_pcuindex, but n-back tasks use mixeddprimeandpcindex.
- 美术卡片、数字卡片：
dprime- 文字卡片、格子卡片：
pc
indices_selected <- indices_memory |>
filter(index_name == "mean_span_pcu" |
(game_name %in% c("美术卡片", "格子卡片") & index_name == "dprime") |
(game_name %in% c("文字卡片", "数字卡片") & index_name == "pc")) |>
pivot_wider_indices() |>
select(-user_id)correlate(indices_selected, quiet = TRUE) |>
rearrange(method = "HC") |>
stretch() |>
mutate(across(c(x, y), as_factor)) |>
ggplot(aes(x, y)) +
geom_tile(aes(fill = r)) +
scico::scale_fill_scico(palette = "bam", midpoint = 0, direction = -1) +
coord_fixed() +
theme_minimal(base_size = 18) +
labs(x = "", y = "", fill = "Pearson's", color = "") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
mds <- indices_selected |>
cor(use = "pairwise") |>
smacof::sim2diss(to.dist = TRUE) |>
smacof::mds(ndim = 2, type = "mspline")
plot(mds)
nfactors_test <- psych::nfactors(indices_selected)
fit <- psych::fa(indices_selected, 3)
psych::fa.diagram(fit)
fit_bifac <- psych::omega(indices_selected, 3, plot = FALSE)
psych::omega.diagram(fit_bifac)
mcmc <- indices_selected |>
mutate(across(.fns = ~ scale(.)[, 1])) |>
befa(verbose = FALSE) |>
post.column.switch() |>
post.sign.switch()hppm <- summary(mcmc, what = "hppm")
hppm |>
pluck("alpha", "m1") |>
as_tibble(rownames = "alpha_term") |>
separate(alpha_term, c(NA, "game_index"), sep = ":") |>
mutate(game_index = reorder(game_index, dedic)) |>
ggplot(aes(game_index, dedic)) +
geom_tile(aes(fill = mean)) +
geom_text(aes(label = round(mean, 2)), color = "white") +
scico::scale_fill_scico(palette = "bam", midpoint = 0, direction = -1) +
coord_fixed() +
theme_minimal(base_size = 18) +
labs(x = "Term", y = "Factor",
title = str_c("Posterior Probability: ", round(hppm$hppm$prob, 2),
", with ", hppm$hppm$nfac, " factors")) +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
Firstly, the model from EFA is tested.
fitted1 <- lavaan::cfa(
'Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted1, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 16 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 36
Number of observations 469
Number of missing patterns 47
Model Test User Model:
Standard Robust
Test Statistic 117.168 115.187
Degrees of freedom 41 41
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.017
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1397.256 1319.621
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.059
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.943 0.941
Tucker-Lewis Index (TLI) 0.924 0.921
Robust Comparative Fit Index (CFI) 0.944
Robust Tucker-Lewis Index (TLI) 0.924
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6192.315 -6192.315
Scaling correction factor 1.024
for the MLR correction
Loglikelihood unrestricted model (H1) -6133.731 -6133.731
Scaling correction factor 1.020
for the MLR correction
Akaike (AIC) 12456.630 12456.630
Bayesian (BIC) 12606.051 12606.051
Sample-size adjusted Bayesian (BIC) 12491.794 12491.794
Root Mean Square Error of Approximation:
RMSEA 0.063 0.062
90 Percent confidence interval - lower 0.050 0.049
90 Percent confidence interval - upper 0.076 0.076
P-value RMSEA <= 0.05 0.053 0.064
Robust RMSEA 0.063
90 Percent confidence interval - lower 0.049
90 Percent confidence interval - upper 0.076
Standardized Root Mean Square Residual:
SRMR 0.036 0.036fitted1_alt <- lavaan::cfa(
'Updating1 =~ `美术卡片` + `数字卡片`
Updating2 =~ `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_alt, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted1_alt, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 20 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 39
Number of observations 469
Number of missing patterns 47
Model Test User Model:
Standard Robust
Test Statistic 65.040 63.632
Degrees of freedom 38 38
P-value (Chi-square) 0.004 0.006
Scaling correction factor 1.022
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1397.256 1319.621
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.059
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.980 0.980
Tucker-Lewis Index (TLI) 0.971 0.971
Robust Comparative Fit Index (CFI) 0.980
Robust Tucker-Lewis Index (TLI) 0.972
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6166.251 -6166.251
Scaling correction factor 1.019
for the MLR correction
Loglikelihood unrestricted model (H1) -6133.731 -6133.731
Scaling correction factor 1.020
for the MLR correction
Akaike (AIC) 12410.501 12410.501
Bayesian (BIC) 12572.375 12572.375
Sample-size adjusted Bayesian (BIC) 12448.597 12448.597
Root Mean Square Error of Approximation:
RMSEA 0.039 0.038
90 Percent confidence interval - lower 0.022 0.021
90 Percent confidence interval - upper 0.055 0.054
P-value RMSEA <= 0.05 0.868 0.891
Robust RMSEA 0.038
90 Percent confidence interval - lower 0.021
90 Percent confidence interval - upper 0.054
Standardized Root Mean Square Residual:
SRMR 0.030 0.030fitted1_alt2 <- lavaan::cfa(
'Updating =~ Updating1 + Updating2
Updating1 =~ `美术卡片` + `数字卡片`
Updating2 =~ `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_alt2, what = "std", edge.color = "black",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted1_alt2, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 33 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 38
Number of observations 469
Number of missing patterns 47
Model Test User Model:
Standard Robust
Test Statistic 65.067 63.695
Degrees of freedom 39 39
P-value (Chi-square) 0.005 0.008
Scaling correction factor 1.022
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1397.256 1319.621
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.059
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.981 0.980
Tucker-Lewis Index (TLI) 0.973 0.972
Robust Comparative Fit Index (CFI) 0.981
Robust Tucker-Lewis Index (TLI) 0.973
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6166.264 -6166.264
Scaling correction factor 1.019
for the MLR correction
Loglikelihood unrestricted model (H1) -6133.731 -6133.731
Scaling correction factor 1.020
for the MLR correction
Akaike (AIC) 12408.528 12408.528
Bayesian (BIC) 12566.251 12566.251
Sample-size adjusted Bayesian (BIC) 12445.647 12445.647
Root Mean Square Error of Approximation:
RMSEA 0.038 0.037
90 Percent confidence interval - lower 0.021 0.019
90 Percent confidence interval - upper 0.053 0.052
P-value RMSEA <= 0.05 0.895 0.915
Robust RMSEA 0.037
90 Percent confidence interval - lower 0.019
90 Percent confidence interval - upper 0.053
Standardized Root Mean Square Residual:
SRMR 0.030 0.030fitted1_bifac <- lavaan::cfa(
'Common =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片` + `幸运小球` + `密码箱` + `顺背数PRO` + `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`
Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE, orthogonal = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_bifac, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0,
bifactor = "Common"
)
lavaan::summary(fitted1_bifac, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 47 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 44
Number of observations 469
Number of missing patterns 47
Model Test User Model:
Standard Robust
Test Statistic 72.027 77.580
Degrees of freedom 33 33
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.928
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1397.256 1319.621
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.059
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.971 0.965
Tucker-Lewis Index (TLI) 0.952 0.941
Robust Comparative Fit Index (CFI) 0.969
Robust Tucker-Lewis Index (TLI) 0.948
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6169.744 -6169.744
Scaling correction factor 1.089
for the MLR correction
Loglikelihood unrestricted model (H1) -6133.731 -6133.731
Scaling correction factor 1.020
for the MLR correction
Akaike (AIC) 12427.488 12427.488
Bayesian (BIC) 12610.115 12610.115
Sample-size adjusted Bayesian (BIC) 12470.467 12470.467
Root Mean Square Error of Approximation:
RMSEA 0.050 0.054
90 Percent confidence interval - lower 0.034 0.038
90 Percent confidence interval - upper 0.066 0.070
P-value RMSEA <= 0.05 0.467 0.332
Robust RMSEA 0.052
90 Percent confidence interval - lower 0.037
90 Percent confidence interval - upper 0.067
Standardized Root Mean Square Residual:
SRMR 0.042 0.042fitted1_higher <- lavaan::cfa(
'Common =~ Updating + VerbalSTM + SpatialSTM
Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_higher, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0,
bifactor = "Common"
)
lavaan::summary(fitted1_higher, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 34 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 36
Number of observations 469
Number of missing patterns 47
Model Test User Model:
Standard Robust
Test Statistic 117.168 115.187
Degrees of freedom 41 41
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.017
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1397.256 1319.621
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.059
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.943 0.941
Tucker-Lewis Index (TLI) 0.924 0.921
Robust Comparative Fit Index (CFI) 0.944
Robust Tucker-Lewis Index (TLI) 0.924
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6192.315 -6192.315
Scaling correction factor 1.024
for the MLR correction
Loglikelihood unrestricted model (H1) -6133.731 -6133.731
Scaling correction factor 1.020
for the MLR correction
Akaike (AIC) 12456.630 12456.630
Bayesian (BIC) 12606.051 12606.051
Sample-size adjusted Bayesian (BIC) 12491.794 12491.794
Root Mean Square Error of Approximation:
RMSEA 0.063 0.062
90 Percent confidence interval - lower 0.050 0.049
90 Percent confidence interval - upper 0.076 0.076
P-value RMSEA <= 0.05 0.053 0.064
Robust RMSEA 0.063
90 Percent confidence interval - lower 0.049
90 Percent confidence interval - upper 0.076
Standardized Root Mean Square Residual:
SRMR 0.036 0.036fitted2 <- lavaan::cfa(
'Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted2, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted2, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 17 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 33
Number of observations 469
Number of missing patterns 43
Model Test User Model:
Standard Robust
Test Statistic 99.969 98.539
Degrees of freedom 32 32
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.015
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1301.556 1234.105
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.055
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.946 0.944
Tucker-Lewis Index (TLI) 0.924 0.921
Robust Comparative Fit Index (CFI) 0.946
Robust Tucker-Lewis Index (TLI) 0.924
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5603.476 -5603.476
Scaling correction factor 1.013
for the MLR correction
Loglikelihood unrestricted model (H1) -5553.491 -5553.491
Scaling correction factor 1.014
for the MLR correction
Akaike (AIC) 11272.952 11272.952
Bayesian (BIC) 11409.921 11409.921
Sample-size adjusted Bayesian (BIC) 11305.186 11305.186
Root Mean Square Error of Approximation:
RMSEA 0.067 0.067
90 Percent confidence interval - lower 0.053 0.052
90 Percent confidence interval - upper 0.082 0.082
P-value RMSEA <= 0.05 0.027 0.032
Robust RMSEA 0.067
90 Percent confidence interval - lower 0.052
90 Percent confidence interval - upper 0.082
Standardized Root Mean Square Residual:
SRMR 0.036 0.036fitted2_alt <- lavaan::cfa(
'Updating1 =~ `美术卡片` + `数字卡片`
Updating2 =~ `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_alt, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted1_alt, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 20 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 39
Number of observations 469
Number of missing patterns 47
Model Test User Model:
Standard Robust
Test Statistic 65.040 63.632
Degrees of freedom 38 38
P-value (Chi-square) 0.004 0.006
Scaling correction factor 1.022
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1397.256 1319.621
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.059
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.980 0.980
Tucker-Lewis Index (TLI) 0.971 0.971
Robust Comparative Fit Index (CFI) 0.980
Robust Tucker-Lewis Index (TLI) 0.972
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6166.251 -6166.251
Scaling correction factor 1.019
for the MLR correction
Loglikelihood unrestricted model (H1) -6133.731 -6133.731
Scaling correction factor 1.020
for the MLR correction
Akaike (AIC) 12410.501 12410.501
Bayesian (BIC) 12572.375 12572.375
Sample-size adjusted Bayesian (BIC) 12448.597 12448.597
Root Mean Square Error of Approximation:
RMSEA 0.039 0.038
90 Percent confidence interval - lower 0.022 0.021
90 Percent confidence interval - upper 0.055 0.054
P-value RMSEA <= 0.05 0.868 0.891
Robust RMSEA 0.038
90 Percent confidence interval - lower 0.021
90 Percent confidence interval - upper 0.054
Standardized Root Mean Square Residual:
SRMR 0.030 0.030fitted2_alt2 <- lavaan::cfa(
'Updating =~ Updating1 + Updating2
Updating1 =~ `美术卡片` + `数字卡片`
Updating2 =~ `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted2_alt2, what = "std", edge.color = "black",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted2_alt2, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 34 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 35
Number of observations 469
Number of missing patterns 43
Model Test User Model:
Standard Robust
Test Statistic 47.868 46.942
Degrees of freedom 30 30
P-value (Chi-square) 0.020 0.025
Scaling correction factor 1.020
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1301.556 1234.105
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.055
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.986 0.986
Tucker-Lewis Index (TLI) 0.979 0.979
Robust Comparative Fit Index (CFI) 0.986
Robust Tucker-Lewis Index (TLI) 0.979
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5577.425 -5577.425
Scaling correction factor 1.009
for the MLR correction
Loglikelihood unrestricted model (H1) -5553.491 -5553.491
Scaling correction factor 1.014
for the MLR correction
Akaike (AIC) 11224.851 11224.851
Bayesian (BIC) 11370.122 11370.122
Sample-size adjusted Bayesian (BIC) 11259.039 11259.039
Root Mean Square Error of Approximation:
RMSEA 0.036 0.035
90 Percent confidence interval - lower 0.014 0.013
90 Percent confidence interval - upper 0.054 0.053
P-value RMSEA <= 0.05 0.897 0.913
Robust RMSEA 0.035
90 Percent confidence interval - lower 0.013
90 Percent confidence interval - upper 0.054
Standardized Root Mean Square Residual:
SRMR 0.029 0.029fitted2_bifac <- lavaan::cfa(
'Common =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片` + `幸运小球` + `密码箱` + `顺背数PRO` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`
Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE, orthogonal = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted2_bifac, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0,
bifactor = "Common"
)
lavaan::summary(fitted2_bifac, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 49 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 40
Number of observations 469
Number of missing patterns 43
Model Test User Model:
Standard Robust
Test Statistic 57.251 80.402
Degrees of freedom 25 25
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.712
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1301.556 1234.105
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.055
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.974 0.953
Tucker-Lewis Index (TLI) 0.954 0.916
Robust Comparative Fit Index (CFI) 0.969
Robust Tucker-Lewis Index (TLI) 0.943
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5582.117 -5582.117
Scaling correction factor 1.202
for the MLR correction
Loglikelihood unrestricted model (H1) -5553.491 -5553.491
Scaling correction factor 1.014
for the MLR correction
Akaike (AIC) 11244.234 11244.234
Bayesian (BIC) 11410.258 11410.258
Sample-size adjusted Bayesian (BIC) 11283.306 11283.306
Root Mean Square Error of Approximation:
RMSEA 0.052 0.069
90 Percent confidence interval - lower 0.035 0.049
90 Percent confidence interval - upper 0.070 0.089
P-value RMSEA <= 0.05 0.385 0.056
Robust RMSEA 0.058
90 Percent confidence interval - lower 0.044
90 Percent confidence interval - upper 0.072
Standardized Root Mean Square Residual:
SRMR 0.042 0.042fitted2_higher <- lavaan::cfa(
'Common =~ Updating + VerbalSTM + SpatialSTM
Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted2_higher, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0,
bifactor = "Common"
)
lavaan::summary(fitted2_higher, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 33 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 33
Number of observations 469
Number of missing patterns 43
Model Test User Model:
Standard Robust
Test Statistic 99.969 98.539
Degrees of freedom 32 32
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.015
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1301.556 1234.105
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.055
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.946 0.944
Tucker-Lewis Index (TLI) 0.924 0.921
Robust Comparative Fit Index (CFI) 0.946
Robust Tucker-Lewis Index (TLI) 0.924
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5603.476 -5603.476
Scaling correction factor 1.013
for the MLR correction
Loglikelihood unrestricted model (H1) -5553.491 -5553.491
Scaling correction factor 1.014
for the MLR correction
Akaike (AIC) 11272.952 11272.952
Bayesian (BIC) 11409.921 11409.921
Sample-size adjusted Bayesian (BIC) 11305.186 11305.186
Root Mean Square Error of Approximation:
RMSEA 0.067 0.067
90 Percent confidence interval - lower 0.053 0.052
90 Percent confidence interval - upper 0.082 0.082
P-value RMSEA <= 0.05 0.027 0.032
Robust RMSEA 0.067
90 Percent confidence interval - lower 0.052
90 Percent confidence interval - upper 0.082
Standardized Root Mean Square Residual:
SRMR 0.036 0.036The covariance estimate for latent variables is not correct. The estimated correlation between “Simple” and “Complex” is larger than 1.
fitted3 <- lavaan::cfa(
'Complex =~ `打靶场` + `蝴蝶照相机` + `幸运小球`
Nback =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
Simple =~ `密码箱` + `顺背数PRO` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
is not positive definite;
use lavInspect(fit, "cov.lv") to investigate.semPlot::semPaths(
fitted3, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted3, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 17 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 33
Number of observations 469
Number of missing patterns 43
Model Test User Model:
Standard Robust
Test Statistic 173.487 172.308
Degrees of freedom 32 32
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.007
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1301.556 1234.105
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.055
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.887 0.882
Tucker-Lewis Index (TLI) 0.842 0.834
Robust Comparative Fit Index (CFI) 0.887
Robust Tucker-Lewis Index (TLI) 0.842
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5640.235 -5640.235
Scaling correction factor 1.020
for the MLR correction
Loglikelihood unrestricted model (H1) -5553.491 -5553.491
Scaling correction factor 1.014
for the MLR correction
Akaike (AIC) 11346.470 11346.470
Bayesian (BIC) 11483.440 11483.440
Sample-size adjusted Bayesian (BIC) 11378.704 11378.704
Root Mean Square Error of Approximation:
RMSEA 0.097 0.097
90 Percent confidence interval - lower 0.083 0.083
90 Percent confidence interval - upper 0.112 0.111
P-value RMSEA <= 0.05 0.000 0.000
Robust RMSEA 0.097
90 Percent confidence interval - lower 0.083
90 Percent confidence interval - upper 0.111
Standardized Root Mean Square Residual:
SRMR 0.053 0.053Not fitted well.
fitted4 <- lavaan::cfa(
'Verbal =~ 数字卡片 + 文字卡片 + 幸运小球 + 密码箱 + 顺背数PRO
Spatial =~ 格子卡片 + 打靶场 + 蝴蝶照相机 + 位置记忆PRO
Object =~ 美术卡片 + 宇宙黑洞',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
is not positive definite;
use lavInspect(fit, "cov.lv") to investigate.semPlot::semPaths(
fitted4, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted4, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 20 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 36
Number of observations 469
Number of missing patterns 47
Model Test User Model:
Standard Robust
Test Statistic 296.008 298.012
Degrees of freedom 41 41
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.993
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1397.256 1319.621
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.059
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.810 0.797
Tucker-Lewis Index (TLI) 0.745 0.727
Robust Comparative Fit Index (CFI) 0.809
Robust Tucker-Lewis Index (TLI) 0.744
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6281.735 -6281.735
Scaling correction factor 1.051
for the MLR correction
Loglikelihood unrestricted model (H1) -6133.731 -6133.731
Scaling correction factor 1.020
for the MLR correction
Akaike (AIC) 12635.470 12635.470
Bayesian (BIC) 12784.891 12784.891
Sample-size adjusted Bayesian (BIC) 12670.634 12670.634
Root Mean Square Error of Approximation:
RMSEA 0.115 0.116
90 Percent confidence interval - lower 0.103 0.103
90 Percent confidence interval - upper 0.128 0.128
P-value RMSEA <= 0.05 0.000 0.000
Robust RMSEA 0.115
90 Percent confidence interval - lower 0.103
90 Percent confidence interval - upper 0.128
Standardized Root Mean Square Residual:
SRMR 0.068 0.068pc indexAll span tasks use
mean_span_pcuindex, but n-back tasks all usepcindex.
indices_selected <- indices_memory |>
filter(index_name %in% c("mean_span_pcu", "pc")) |>
pivot_wider_indices() |>
select(-user_id)correlate(indices_selected, quiet = TRUE) |>
rearrange(method = "HC") |>
stretch() |>
mutate(across(c(x, y), as_factor)) |>
ggplot(aes(x, y)) +
geom_tile(aes(fill = r)) +
scico::scale_fill_scico(palette = "bam", midpoint = 0, direction = -1) +
coord_fixed() +
theme_minimal(base_size = 18) +
labs(x = "", y = "", fill = "Pearson's", color = "") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
mds <- indices_selected |>
cor(use = "pairwise") |>
smacof::sim2diss(to.dist = TRUE) |>
smacof::mds(ndim = 2, type = "mspline")
plot(mds)
nfactors_test <- psych::nfactors(indices_selected)
fit <- psych::fa(indices_selected, 3)
psych::fa.diagram(fit)
fit_bifac <- psych::omega(indices_selected, 3, plot = FALSE)
psych::omega.diagram(fit_bifac)
mcmc <- indices_selected |>
mutate(across(.fns = ~ scale(.)[, 1])) |>
befa(verbose = FALSE) |>
post.column.switch() |>
post.sign.switch()hppm <- summary(mcmc, what = "hppm")
hppm |>
pluck("alpha", "m1") |>
as_tibble(rownames = "alpha_term") |>
separate(alpha_term, c(NA, "game_index"), sep = ":") |>
mutate(game_index = reorder(game_index, dedic)) |>
ggplot(aes(game_index, dedic)) +
geom_tile(aes(fill = mean)) +
geom_text(aes(label = round(mean, 2)), color = "white") +
scico::scale_fill_scico(palette = "bam", midpoint = 0, direction = -1) +
coord_fixed() +
theme_minimal(base_size = 18) +
labs(x = "Term", y = "Factor",
title = str_c("Posterior Probability: ", round(hppm$hppm$prob, 2),
", with ", hppm$hppm$nfac, " factors")) +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
Firstly, the model from EFA is tested.
fitted1 <- lavaan::cfa(
'Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted1, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 18 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 36
Number of observations 469
Number of missing patterns 45
Model Test User Model:
Standard Robust
Test Statistic 119.456 116.993
Degrees of freedom 41 41
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.021
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1417.507 1333.075
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.063
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.942 0.941
Tucker-Lewis Index (TLI) 0.923 0.920
Robust Comparative Fit Index (CFI) 0.943
Robust Tucker-Lewis Index (TLI) 0.923
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6197.522 -6197.522
Scaling correction factor 1.025
for the MLR correction
Loglikelihood unrestricted model (H1) -6137.794 -6137.794
Scaling correction factor 1.023
for the MLR correction
Akaike (AIC) 12467.044 12467.044
Bayesian (BIC) 12616.466 12616.466
Sample-size adjusted Bayesian (BIC) 12502.209 12502.209
Root Mean Square Error of Approximation:
RMSEA 0.064 0.063
90 Percent confidence interval - lower 0.051 0.050
90 Percent confidence interval - upper 0.077 0.076
P-value RMSEA <= 0.05 0.042 0.053
Robust RMSEA 0.064
90 Percent confidence interval - lower 0.050
90 Percent confidence interval - upper 0.077
Standardized Root Mean Square Residual:
SRMR 0.037 0.037fitted1_alt <- lavaan::cfa(
'Updating1 =~ `美术卡片` + `数字卡片`
Updating2 =~ `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_alt, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted1_alt, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 21 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 39
Number of observations 469
Number of missing patterns 45
Model Test User Model:
Standard Robust
Test Statistic 67.870 66.281
Degrees of freedom 38 38
P-value (Chi-square) 0.002 0.003
Scaling correction factor 1.024
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1417.507 1333.075
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.063
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.978 0.978
Tucker-Lewis Index (TLI) 0.968 0.968
Robust Comparative Fit Index (CFI) 0.979
Robust Tucker-Lewis Index (TLI) 0.969
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6171.729 -6171.729
Scaling correction factor 1.021
for the MLR correction
Loglikelihood unrestricted model (H1) -6137.794 -6137.794
Scaling correction factor 1.023
for the MLR correction
Akaike (AIC) 12421.459 12421.459
Bayesian (BIC) 12583.332 12583.332
Sample-size adjusted Bayesian (BIC) 12459.554 12459.554
Root Mean Square Error of Approximation:
RMSEA 0.041 0.040
90 Percent confidence interval - lower 0.025 0.023
90 Percent confidence interval - upper 0.056 0.055
P-value RMSEA <= 0.05 0.820 0.851
Robust RMSEA 0.040
90 Percent confidence interval - lower 0.023
90 Percent confidence interval - upper 0.056
Standardized Root Mean Square Residual:
SRMR 0.031 0.031fitted1_alt2 <- lavaan::cfa(
'Updating =~ Updating1 + Updating2
Updating1 =~ `美术卡片` + `数字卡片`
Updating2 =~ `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_alt2, what = "std", edge.color = "black",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted1_alt2, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 33 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 38
Number of observations 469
Number of missing patterns 45
Model Test User Model:
Standard Robust
Test Statistic 68.030 66.505
Degrees of freedom 39 39
P-value (Chi-square) 0.003 0.004
Scaling correction factor 1.023
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1417.507 1333.075
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.063
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.979 0.978
Tucker-Lewis Index (TLI) 0.970 0.970
Robust Comparative Fit Index (CFI) 0.979
Robust Tucker-Lewis Index (TLI) 0.971
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6171.809 -6171.809
Scaling correction factor 1.022
for the MLR correction
Loglikelihood unrestricted model (H1) -6137.794 -6137.794
Scaling correction factor 1.023
for the MLR correction
Akaike (AIC) 12419.618 12419.618
Bayesian (BIC) 12577.341 12577.341
Sample-size adjusted Bayesian (BIC) 12456.737 12456.737
Root Mean Square Error of Approximation:
RMSEA 0.040 0.039
90 Percent confidence interval - lower 0.023 0.022
90 Percent confidence interval - upper 0.055 0.054
P-value RMSEA <= 0.05 0.851 0.878
Robust RMSEA 0.039
90 Percent confidence interval - lower 0.022
90 Percent confidence interval - upper 0.055
Standardized Root Mean Square Residual:
SRMR 0.031 0.031fitted1_bifac <- lavaan::cfa(
'Common =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片` + `幸运小球` + `密码箱` + `顺背数PRO` + `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`
Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE, orthogonal = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_bifac, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0,
bifactor = "Common"
)
lavaan::summary(fitted1_bifac, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 42 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 44
Number of observations 469
Number of missing patterns 45
Model Test User Model:
Standard Robust
Test Statistic 76.215 86.440
Degrees of freedom 33 33
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.882
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1417.507 1333.075
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.063
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.968 0.958
Tucker-Lewis Index (TLI) 0.947 0.930
Robust Comparative Fit Index (CFI) 0.965
Robust Tucker-Lewis Index (TLI) 0.942
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6175.902 -6175.902
Scaling correction factor 1.128
for the MLR correction
Loglikelihood unrestricted model (H1) -6137.794 -6137.794
Scaling correction factor 1.023
for the MLR correction
Akaike (AIC) 12439.804 12439.804
Bayesian (BIC) 12622.430 12622.430
Sample-size adjusted Bayesian (BIC) 12482.783 12482.783
Root Mean Square Error of Approximation:
RMSEA 0.053 0.059
90 Percent confidence interval - lower 0.037 0.043
90 Percent confidence interval - upper 0.068 0.075
P-value RMSEA <= 0.05 0.360 0.173
Robust RMSEA 0.055
90 Percent confidence interval - lower 0.041
90 Percent confidence interval - upper 0.070
Standardized Root Mean Square Residual:
SRMR 0.046 0.046fitted1_higher <- lavaan::cfa(
'Common =~ Updating + VerbalSTM + SpatialSTM
Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_higher, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0,
bifactor = "Common"
)
lavaan::summary(fitted1_higher, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 34 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 36
Number of observations 469
Number of missing patterns 45
Model Test User Model:
Standard Robust
Test Statistic 119.456 116.993
Degrees of freedom 41 41
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.021
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1417.507 1333.075
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.063
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.942 0.941
Tucker-Lewis Index (TLI) 0.923 0.920
Robust Comparative Fit Index (CFI) 0.943
Robust Tucker-Lewis Index (TLI) 0.923
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6197.522 -6197.522
Scaling correction factor 1.025
for the MLR correction
Loglikelihood unrestricted model (H1) -6137.794 -6137.794
Scaling correction factor 1.023
for the MLR correction
Akaike (AIC) 12467.044 12467.044
Bayesian (BIC) 12616.466 12616.466
Sample-size adjusted Bayesian (BIC) 12502.209 12502.209
Root Mean Square Error of Approximation:
RMSEA 0.064 0.063
90 Percent confidence interval - lower 0.051 0.050
90 Percent confidence interval - upper 0.077 0.076
P-value RMSEA <= 0.05 0.042 0.053
Robust RMSEA 0.064
90 Percent confidence interval - lower 0.050
90 Percent confidence interval - upper 0.077
Standardized Root Mean Square Residual:
SRMR 0.037 0.037fitted2 <- lavaan::cfa(
'Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted2, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted2, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 17 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 33
Number of observations 469
Number of missing patterns 40
Model Test User Model:
Standard Robust
Test Statistic 102.626 100.460
Degrees of freedom 32 32
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.022
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1322.205 1245.873
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.061
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.945 0.943
Tucker-Lewis Index (TLI) 0.922 0.920
Robust Comparative Fit Index (CFI) 0.945
Robust Tucker-Lewis Index (TLI) 0.923
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5608.669 -5608.669
Scaling correction factor 1.013
for the MLR correction
Loglikelihood unrestricted model (H1) -5557.356 -5557.356
Scaling correction factor 1.017
for the MLR correction
Akaike (AIC) 11283.338 11283.338
Bayesian (BIC) 11420.308 11420.308
Sample-size adjusted Bayesian (BIC) 11315.573 11315.573
Root Mean Square Error of Approximation:
RMSEA 0.069 0.068
90 Percent confidence interval - lower 0.054 0.053
90 Percent confidence interval - upper 0.084 0.083
P-value RMSEA <= 0.05 0.019 0.024
Robust RMSEA 0.068
90 Percent confidence interval - lower 0.053
90 Percent confidence interval - upper 0.084
Standardized Root Mean Square Residual:
SRMR 0.036 0.036fitted2_alt <- lavaan::cfa(
'Updating1 =~ `美术卡片` + `数字卡片`
Updating2 =~ `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted1_alt, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted1_alt, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 21 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 39
Number of observations 469
Number of missing patterns 45
Model Test User Model:
Standard Robust
Test Statistic 67.870 66.281
Degrees of freedom 38 38
P-value (Chi-square) 0.002 0.003
Scaling correction factor 1.024
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1417.507 1333.075
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.063
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.978 0.978
Tucker-Lewis Index (TLI) 0.968 0.968
Robust Comparative Fit Index (CFI) 0.979
Robust Tucker-Lewis Index (TLI) 0.969
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6171.729 -6171.729
Scaling correction factor 1.021
for the MLR correction
Loglikelihood unrestricted model (H1) -6137.794 -6137.794
Scaling correction factor 1.023
for the MLR correction
Akaike (AIC) 12421.459 12421.459
Bayesian (BIC) 12583.332 12583.332
Sample-size adjusted Bayesian (BIC) 12459.554 12459.554
Root Mean Square Error of Approximation:
RMSEA 0.041 0.040
90 Percent confidence interval - lower 0.025 0.023
90 Percent confidence interval - upper 0.056 0.055
P-value RMSEA <= 0.05 0.820 0.851
Robust RMSEA 0.040
90 Percent confidence interval - lower 0.023
90 Percent confidence interval - upper 0.056
Standardized Root Mean Square Residual:
SRMR 0.031 0.031fitted2_alt2 <- lavaan::cfa(
'Updating =~ Updating1 + Updating2
Updating1 =~ `美术卡片` + `数字卡片`
Updating2 =~ `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted2_alt2, what = "std", edge.color = "black",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted2_alt2, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 35 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 35
Number of observations 469
Number of missing patterns 40
Model Test User Model:
Standard Robust
Test Statistic 51.226 50.023
Degrees of freedom 30 30
P-value (Chi-square) 0.009 0.012
Scaling correction factor 1.024
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1322.205 1245.873
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.061
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.983 0.983
Tucker-Lewis Index (TLI) 0.975 0.975
Robust Comparative Fit Index (CFI) 0.984
Robust Tucker-Lewis Index (TLI) 0.976
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5582.969 -5582.969
Scaling correction factor 1.011
for the MLR correction
Loglikelihood unrestricted model (H1) -5557.356 -5557.356
Scaling correction factor 1.017
for the MLR correction
Akaike (AIC) 11235.937 11235.937
Bayesian (BIC) 11381.209 11381.209
Sample-size adjusted Bayesian (BIC) 11270.126 11270.126
Root Mean Square Error of Approximation:
RMSEA 0.039 0.038
90 Percent confidence interval - lower 0.019 0.018
90 Percent confidence interval - upper 0.057 0.055
P-value RMSEA <= 0.05 0.838 0.865
Robust RMSEA 0.038
90 Percent confidence interval - lower 0.018
90 Percent confidence interval - upper 0.056
Standardized Root Mean Square Residual:
SRMR 0.029 0.029fitted2_bifac <- lavaan::cfa(
'Common =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片` + `幸运小球` + `密码箱` + `顺背数PRO` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`
Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE, orthogonal = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted2_bifac, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0,
bifactor = "Common"
)
lavaan::summary(fitted2_bifac, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 46 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 40
Number of observations 469
Number of missing patterns 40
Model Test User Model:
Standard Robust
Test Statistic 62.874 72.175
Degrees of freedom 25 25
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.871
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1322.205 1245.873
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.061
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.970 0.961
Tucker-Lewis Index (TLI) 0.947 0.929
Robust Comparative Fit Index (CFI) 0.968
Robust Tucker-Lewis Index (TLI) 0.942
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5588.793 -5588.793
Scaling correction factor 1.108
for the MLR correction
Loglikelihood unrestricted model (H1) -5557.356 -5557.356
Scaling correction factor 1.017
for the MLR correction
Akaike (AIC) 11257.586 11257.586
Bayesian (BIC) 11423.610 11423.610
Sample-size adjusted Bayesian (BIC) 11296.659 11296.659
Root Mean Square Error of Approximation:
RMSEA 0.057 0.063
90 Percent confidence interval - lower 0.039 0.045
90 Percent confidence interval - upper 0.075 0.082
P-value RMSEA <= 0.05 0.241 0.105
Robust RMSEA 0.059
90 Percent confidence interval - lower 0.044
90 Percent confidence interval - upper 0.075
Standardized Root Mean Square Residual:
SRMR 0.046 0.046fitted2_higher <- lavaan::cfa(
'Common =~ Updating + VerbalSTM + SpatialSTM
Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fitted2_higher, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0,
bifactor = "Common"
)
lavaan::summary(fitted2_higher, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 34 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 33
Number of observations 469
Number of missing patterns 40
Model Test User Model:
Standard Robust
Test Statistic 102.626 100.460
Degrees of freedom 32 32
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.022
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1322.205 1245.873
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.061
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.945 0.943
Tucker-Lewis Index (TLI) 0.922 0.920
Robust Comparative Fit Index (CFI) 0.945
Robust Tucker-Lewis Index (TLI) 0.923
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5608.669 -5608.669
Scaling correction factor 1.013
for the MLR correction
Loglikelihood unrestricted model (H1) -5557.356 -5557.356
Scaling correction factor 1.017
for the MLR correction
Akaike (AIC) 11283.338 11283.338
Bayesian (BIC) 11420.308 11420.308
Sample-size adjusted Bayesian (BIC) 11315.573 11315.573
Root Mean Square Error of Approximation:
RMSEA 0.069 0.068
90 Percent confidence interval - lower 0.054 0.053
90 Percent confidence interval - upper 0.084 0.083
P-value RMSEA <= 0.05 0.019 0.024
Robust RMSEA 0.068
90 Percent confidence interval - lower 0.053
90 Percent confidence interval - upper 0.084
Standardized Root Mean Square Residual:
SRMR 0.036 0.036The covariance estimate for latent variables is not correct. The estimated correlation between “Simple” and “Complex” is larger than 1.
fitted3 <- lavaan::cfa(
'Complex =~ `打靶场` + `蝴蝶照相机` + `幸运小球`
Nback =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
Simple =~ `密码箱` + `顺背数PRO` + `位置记忆PRO`',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
is not positive definite;
use lavInspect(fit, "cov.lv") to investigate.semPlot::semPaths(
fitted3, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted3, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 18 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 33
Number of observations 469
Number of missing patterns 40
Model Test User Model:
Standard Robust
Test Statistic 175.560 172.586
Degrees of freedom 32 32
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.017
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1322.205 1245.873
Degrees of freedom 45 45
P-value 0.000 0.000
Scaling correction factor 1.061
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.888 0.883
Tucker-Lewis Index (TLI) 0.842 0.835
Robust Comparative Fit Index (CFI) 0.888
Robust Tucker-Lewis Index (TLI) 0.842
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5645.136 -5645.136
Scaling correction factor 1.017
for the MLR correction
Loglikelihood unrestricted model (H1) -5557.356 -5557.356
Scaling correction factor 1.017
for the MLR correction
Akaike (AIC) 11356.271 11356.271
Bayesian (BIC) 11493.241 11493.241
Sample-size adjusted Bayesian (BIC) 11388.506 11388.506
Root Mean Square Error of Approximation:
RMSEA 0.098 0.097
90 Percent confidence interval - lower 0.084 0.083
90 Percent confidence interval - upper 0.112 0.111
P-value RMSEA <= 0.05 0.000 0.000
Robust RMSEA 0.098
90 Percent confidence interval - lower 0.084
90 Percent confidence interval - upper 0.112
Standardized Root Mean Square Residual:
SRMR 0.054 0.054Not fitted well.
fitted4 <- lavaan::cfa(
'Verbal =~ 数字卡片 + 文字卡片 + 幸运小球 + 密码箱 + 顺背数PRO
Spatial =~ 格子卡片 + 打靶场 + 蝴蝶照相机 + 位置记忆PRO
Object =~ 美术卡片 + 宇宙黑洞',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
is not positive definite;
use lavInspect(fit, "cov.lv") to investigate.semPlot::semPaths(
fitted4, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fitted4, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 20 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 36
Number of observations 469
Number of missing patterns 45
Model Test User Model:
Standard Robust
Test Statistic 318.493 323.033
Degrees of freedom 41 41
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.986
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1417.507 1333.075
Degrees of freedom 55 55
P-value 0.000 0.000
Scaling correction factor 1.063
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.796 0.779
Tucker-Lewis Index (TLI) 0.727 0.704
Robust Comparative Fit Index (CFI) 0.795
Robust Tucker-Lewis Index (TLI) 0.726
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6297.041 -6297.041
Scaling correction factor 1.065
for the MLR correction
Loglikelihood unrestricted model (H1) -6137.794 -6137.794
Scaling correction factor 1.023
for the MLR correction
Akaike (AIC) 12666.082 12666.082
Bayesian (BIC) 12815.503 12815.503
Sample-size adjusted Bayesian (BIC) 12701.247 12701.247
Root Mean Square Error of Approximation:
RMSEA 0.120 0.121
90 Percent confidence interval - lower 0.108 0.109
90 Percent confidence interval - upper 0.133 0.134
P-value RMSEA <= 0.05 0.000 0.000
Robust RMSEA 0.120
90 Percent confidence interval - lower 0.108
90 Percent confidence interval - upper 0.133
Standardized Root Mean Square Residual:
SRMR 0.070 0.070indices_selected <- indices_clean |>
filter(
check_result == "target",
dimension %in% c("reasoning", "complex span", "working memory", "short term memory"),
!game_name %in% c("远距离联想", "人工语言-中级", "各得其所", "魔术师终极")
) |>
pivot_wider_indices() |>
select(-user_id)The included tasks:
correlate(indices_selected, quiet = TRUE) |>
rearrange(method = "HC") |>
stretch() |>
mutate(across(c(x, y), as_factor)) |>
ggplot(aes(x, y)) +
geom_tile(aes(fill = r)) +
scico::scale_fill_scico(palette = "bam", midpoint = 0, direction = -1) +
coord_fixed() +
theme_minimal(base_size = 18) +
labs(x = "", y = "", fill = "Pearson's", color = "") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
mds <- indices_selected |>
cor(use = "pairwise") |>
smacof::sim2diss(to.dist = TRUE) |>
smacof::mds(ndim = 2, type = "mspline")
# plot(mds, plot.type = "Shepard", main = "Shepard Diagram (Ratio Transformation)")
# par(family = "SimHei")
plot(mds)
nfactors_test <- psych::nfactors(indices_selected)
fit <- psych::fa(indices_selected, 4)
psych::fa.diagram(fit)
fit_bifac <- psych::omega(indices_selected, 4, plot = FALSE)
psych::omega.diagram(fit_bifac)
mcmc <- indices_selected |>
mutate(across(.fns = ~ scale(.)[, 1])) |>
befa(verbose = FALSE) |>
post.column.switch() |>
post.sign.switch()hppm <- summary(mcmc, what = "hppm")
hppm |>
pluck("alpha", "m1") |>
as_tibble(rownames = "alpha_term") |>
separate(alpha_term, c(NA, "game_index"), sep = ":") |>
mutate(game_index = reorder(game_index, dedic)) |>
ggplot(aes(game_index, dedic)) +
geom_tile(aes(fill = mean)) +
geom_text(aes(label = round(mean, 2)), color = "white") +
scico::scale_fill_scico(palette = "bam", midpoint = 0, direction = -1) +
coord_fixed() +
theme_minimal(base_size = 18) +
labs(x = "Term", y = "Factor",
title = str_c("Posterior Probability: ", round(hppm$hppm$prob, 2),
", with ", hppm$hppm$nfac, " factors")) +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
fit_result <- lavaan::cfa(
'Updating =~ `美术卡片` + `数字卡片` + `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`
Reasoning =~ 三维心理旋转测试 + 图形推理 + 图形折叠',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fit_result, what = "std", edge.color = "black", layout = "tree2",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fit_result, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 21 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 48
Number of observations 469
Number of missing patterns 72
Model Test User Model:
Standard Robust
Test Statistic 172.314 172.556
Degrees of freedom 71 71
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.999
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1615.500 1546.634
Degrees of freedom 91 91
P-value 0.000 0.000
Scaling correction factor 1.045
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.934 0.930
Tucker-Lewis Index (TLI) 0.915 0.911
Robust Comparative Fit Index (CFI) 0.933
Robust Tucker-Lewis Index (TLI) 0.915
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -7811.990 -7811.990
Scaling correction factor 1.051
for the MLR correction
Loglikelihood unrestricted model (H1) -7725.833 -7725.833
Scaling correction factor 1.020
for the MLR correction
Akaike (AIC) 15719.980 15719.980
Bayesian (BIC) 15919.209 15919.209
Sample-size adjusted Bayesian (BIC) 15766.867 15766.867
Root Mean Square Error of Approximation:
RMSEA 0.055 0.055
90 Percent confidence interval - lower 0.045 0.045
90 Percent confidence interval - upper 0.066 0.066
P-value RMSEA <= 0.05 0.200 0.197
Robust RMSEA 0.055
90 Percent confidence interval - lower 0.045
90 Percent confidence interval - upper 0.066
Standardized Root Mean Square Residual:
SRMR 0.040 0.040fit_result_alt <- lavaan::cfa(
'Updating =~ Updating1 + Updating2
Updating1 =~ `美术卡片` + `数字卡片`
Updating2 =~ `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `宇宙黑洞` + `打靶场` + `蝴蝶照相机` + `位置记忆PRO`
Reasoning =~ 三维心理旋转测试 + 图形推理 + 图形折叠',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fit_result_alt, what = "std", edge.color = "black",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fit_result_alt, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 35 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 50
Number of observations 469
Number of missing patterns 72
Model Test User Model:
Standard Robust
Test Statistic 121.402 121.672
Degrees of freedom 69 69
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.998
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1615.500 1546.634
Degrees of freedom 91 91
P-value 0.000 0.000
Scaling correction factor 1.045
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.966 0.964
Tucker-Lewis Index (TLI) 0.955 0.952
Robust Comparative Fit Index (CFI) 0.965
Robust Tucker-Lewis Index (TLI) 0.954
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -7786.534 -7786.534
Scaling correction factor 1.050
for the MLR correction
Loglikelihood unrestricted model (H1) -7725.833 -7725.833
Scaling correction factor 1.020
for the MLR correction
Akaike (AIC) 15673.068 15673.068
Bayesian (BIC) 15880.598 15880.598
Sample-size adjusted Bayesian (BIC) 15721.908 15721.908
Root Mean Square Error of Approximation:
RMSEA 0.040 0.040
90 Percent confidence interval - lower 0.028 0.028
90 Percent confidence interval - upper 0.052 0.052
P-value RMSEA <= 0.05 0.914 0.911
Robust RMSEA 0.040
90 Percent confidence interval - lower 0.028
90 Percent confidence interval - upper 0.052
Standardized Root Mean Square Residual:
SRMR 0.036 0.036fit_result_high_order <- lavaan::cfa(
'WM =~ Updating + VerbalSTM + SpatialSTM
Updating =~ Updating1 + Updating2
Updating1 =~ `美术卡片` + `数字卡片`
Updating2 =~ `格子卡片` + `文字卡片`
# AscMem =~ `人工语言-中级` + `欢乐餐厅` + 图片记忆
VerbalSTM =~ `幸运小球` + `密码箱` + `顺背数PRO`
SpatialSTM =~ `打靶场` + `蝴蝶照相机` + `位置记忆PRO`
Reasoning =~ 三维心理旋转测试 + 图形推理 + 图形折叠',
indices_selected, std.lv = TRUE, std.ov = TRUE,
estimator = "MLR", missing = "ml"
)
semPlot::semPaths(
fit_result_high_order, what = "std", edge.color = "black",
sizeMan = 6, sizeLat = 8, edge.label.cex = 0.6, intercepts = FALSE,
nCharEdges = 5, esize = 1, trans = 1, nCharNodes = 0
)
lavaan::summary(fit_result_high_order, fit.measures = TRUE, estimates = FALSE)lavaan 0.6-11 ended normally after 49 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 45
Number of observations 469
Number of missing patterns 68
Model Test User Model:
Standard Robust
Test Statistic 109.216 109.773
Degrees of freedom 59 59
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.995
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1511.617 1452.531
Degrees of freedom 78 78
P-value 0.000 0.000
Scaling correction factor 1.041
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.965 0.963
Tucker-Lewis Index (TLI) 0.954 0.951
Robust Comparative Fit Index (CFI) 0.965
Robust Tucker-Lewis Index (TLI) 0.953
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -7204.293 -7204.293
Scaling correction factor 1.041
for the MLR correction
Loglikelihood unrestricted model (H1) -7149.685 -7149.685
Scaling correction factor 1.015
for the MLR correction
Akaike (AIC) 14498.586 14498.586
Bayesian (BIC) 14685.363 14685.363
Sample-size adjusted Bayesian (BIC) 14542.543 14542.543
Root Mean Square Error of Approximation:
RMSEA 0.043 0.043
90 Percent confidence interval - lower 0.030 0.030
90 Percent confidence interval - upper 0.055 0.055
P-value RMSEA <= 0.05 0.830 0.821
Robust RMSEA 0.043
90 Percent confidence interval - lower 0.030
90 Percent confidence interval - upper 0.055
Standardized Root Mean Square Residual:
SRMR 0.039 0.039