# data - TIMSS, coutry - Canada
library(foreign)
library(dplyr)
data = read.spss("BSGCANM6.sav", to.data.frame=TRUE)
#names(data)
dat <- data %>% select(BSBS21A, BSBS21B, BSBS21C, BSBS21D, BSBS21E, BSBS21F, BSBS21G, BSBS21H, BSBS21I,
BSBS23A, BSBS23B, BSBS23C, BSBS23D, BSBS23E, BSBS23F, BSBS23G, BSBS23H,
BSBS24A, BSBS24B, BSBS24C, BSBS24D, BSBS24E, BSBS24F, BSBS24G, BSBS24H, BSBS24I)
dat1 <- as.data.frame(lapply(dat, as.numeric))
dat1 <- cbind(dat1, data$BSBG01)
names(dat1) <- c("BSBS21A", "BSBS21B", "BSBS21C", "BSBS21D", "BSBS21E", "BSBS21F", "BSBS21G", "BSBS21H", "BSBS21I",
"BSBS23A", "BSBS23B", "BSBS23C", "BSBS23D", "BSBS23E", "BSBS23F", "BSBS23G", "BSBS23H",
"BSBS24A", "BSBS24B", "BSBS24C", "BSBS24D", "BSBS24E", "BSBS24F", "BSBS24G", "BSBS24H", "BSBS24I", "gender")
dat1 <- dat1 %>% na.omit(dat1$gender)
#summary(dat1)
#names(dat) <- c("enjoy", "wish_not", "boring", "learn_intrst", #"like_science", "look_forw", "___", "___", "favourite",
# "tchr_exp_do", "tchr_easy_undrstnd", #"intrst_tchr_say", "intrst_do", "tchr_clear_answ", "tchr_expl_good", #"tchr_show_learn", "dif_help", "tel_how_better", "tchr_listen",
# "us_do_well", "difficult", "not_strong", #"learn_quick", "makes_nerv")# Define the CFA model
library(lavaan)## This is lavaan 0.6-6## lavaan is BETA software! Please report any bugs.model_cfa <- 'like_learning =~ BSBS21A + BSBS21B + BSBS21C + BSBS21D + BSBS21E + BSBS21F + BSBS21G + BSBS21H + BSBS21I
confident =~ BSBS23A + BSBS23B + BSBS23C + BSBS23D + BSBS23E + BSBS23F + BSBS23G + BSBS23H
value =~ BSBS24A + BSBS24B + BSBS24C + BSBS24D + BSBS24E + BSBS24F + BSBS24G + BSBS24H + BSBS24I'Test statistic = 16551.775 Degrees of freedom = 592 pvalue = 0.000 CFI = 0.888 TLI = 0.877 RMSEA = 0.083 AIC = 401285.533 BIC = 401898.762 SRMR = 0.057
estimate coefficients differ, but not too much.
science_cfa_1 <- cfa(model = model_cfa, data = dat1, group="gender")
summary(science_cfa_1,fit.measures=TRUE)## lavaan 0.6-6 ended normally after 53 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 162
##
## Number of observations per group:
## Girl 3995
## Boy 3815
##
## Model Test User Model:
##
## Test statistic 16551.775
## Degrees of freedom 592
## P-value (Chi-square) 0.000
## Test statistic for each group:
## Girl 7973.715
## Boy 8578.060
##
## Model Test Baseline Model:
##
## Test statistic 143641.597
## Degrees of freedom 650
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.888
## Tucker-Lewis Index (TLI) 0.877
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -200480.766
## Loglikelihood unrestricted model (H1) -192204.879
##
## Akaike (AIC) 401285.533
## Bayesian (BIC) 402413.565
## Sample-size adjusted Bayesian (BIC) 401898.762
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.083
## 90 Percent confidence interval - lower 0.082
## 90 Percent confidence interval - upper 0.084
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.057
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [Girl]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## like_learning =~
## BSBS21A 1.000
## BSBS21B -0.841 0.017 -48.733 0.000
## BSBS21C -0.896 0.015 -57.985 0.000
## BSBS21D 0.750 0.013 57.211 0.000
## BSBS21E 1.076 0.012 88.022 0.000
## BSBS21F 1.087 0.013 80.672 0.000
## BSBS21G 0.536 0.013 40.672 0.000
## BSBS21H 0.499 0.015 33.174 0.000
## BSBS21I 1.159 0.015 76.897 0.000
## confident =~
## BSBS23A 1.000
## BSBS23B -1.126 0.024 -47.380 0.000
## BSBS23C -1.359 0.026 -53.162 0.000
## BSBS23D 1.178 0.022 53.073 0.000
## BSBS23E 1.157 0.024 48.954 0.000
## BSBS23F 0.935 0.025 37.830 0.000
## BSBS23G -1.156 0.024 -48.155 0.000
## BSBS23H -1.203 0.025 -47.378 0.000
## value =~
## BSBS24A 1.000
## BSBS24B 1.065 0.024 44.035 0.000
## BSBS24C 1.218 0.023 52.883 0.000
## BSBS24D 1.355 0.026 52.126 0.000
## BSBS24E 1.349 0.028 47.398 0.000
## BSBS24F 1.093 0.023 47.358 0.000
## BSBS24G 1.134 0.022 51.403 0.000
## BSBS24H 0.794 0.020 39.983 0.000
## BSBS24I 0.807 0.018 45.157 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## like_learning ~~
## confident 0.327 0.010 31.403 0.000
## value 0.273 0.010 26.923 0.000
## confident ~~
## value 0.164 0.007 22.590 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A 1.973 0.014 141.364 0.000
## .BSBS21B 2.766 0.016 175.471 0.000
## .BSBS21C 2.845 0.015 189.792 0.000
## .BSBS21D 1.718 0.013 135.933 0.000
## .BSBS21E 1.989 0.014 137.211 0.000
## .BSBS21F 2.207 0.015 144.984 0.000
## .BSBS21G 1.617 0.011 141.102 0.000
## .BSBS21H 1.581 0.013 126.004 0.000
## .BSBS21I 2.387 0.017 143.886 0.000
## .BSBS23A 1.840 0.012 156.251 0.000
## .BSBS23B 2.962 0.014 211.634 0.000
## .BSBS23C 2.686 0.015 175.534 0.000
## .BSBS23D 2.149 0.013 161.769 0.000
## .BSBS23E 2.434 0.014 174.147 0.000
## .BSBS23F 2.436 0.014 171.614 0.000
## .BSBS23G 3.022 0.014 213.368 0.000
## .BSBS23H 2.805 0.015 187.561 0.000
## .BSBS24A 1.865 0.013 142.376 0.000
## .BSBS24B 2.163 0.015 148.483 0.000
## .BSBS24C 1.774 0.014 126.495 0.000
## .BSBS24D 1.971 0.016 124.675 0.000
## .BSBS24E 2.330 0.017 135.333 0.000
## .BSBS24F 1.886 0.014 135.211 0.000
## .BSBS24G 1.718 0.013 128.172 0.000
## .BSBS24H 1.605 0.012 134.884 0.000
## .BSBS24I 1.505 0.011 139.652 0.000
## like_learning 0.000
## confident 0.000
## value 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A 0.171 0.005 36.698 0.000
## .BSBS21B 0.563 0.013 43.004 0.000
## .BSBS21C 0.410 0.010 42.049 0.000
## .BSBS21D 0.297 0.007 42.144 0.000
## .BSBS21E 0.136 0.004 33.106 0.000
## .BSBS21F 0.208 0.006 36.948 0.000
## .BSBS21G 0.350 0.008 43.593 0.000
## .BSBS21H 0.478 0.011 43.996 0.000
## .BSBS21I 0.285 0.007 38.283 0.000
## .BSBS23A 0.228 0.006 39.013 0.000
## .BSBS23B 0.370 0.009 40.257 0.000
## .BSBS23C 0.335 0.009 37.529 0.000
## .BSBS23D 0.254 0.007 37.586 0.000
## .BSBS23E 0.345 0.009 39.669 0.000
## .BSBS23F 0.520 0.012 42.526 0.000
## .BSBS23G 0.367 0.009 39.979 0.000
## .BSBS23H 0.422 0.010 40.257 0.000
## .BSBS24A 0.317 0.008 40.769 0.000
## .BSBS24B 0.430 0.010 41.409 0.000
## .BSBS24C 0.239 0.006 36.935 0.000
## .BSBS24D 0.323 0.009 37.580 0.000
## .BSBS24E 0.514 0.013 40.274 0.000
## .BSBS24F 0.338 0.008 40.290 0.000
## .BSBS24G 0.244 0.006 38.123 0.000
## .BSBS24H 0.334 0.008 42.347 0.000
## .BSBS24I 0.224 0.005 41.076 0.000
## like_learning 0.607 0.017 35.333 0.000
## confident 0.325 0.012 27.951 0.000
## value 0.368 0.014 26.364 0.000
##
##
## Group 2 [Boy]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## like_learning =~
## BSBS21A 1.000
## BSBS21B -0.731 0.019 -37.874 0.000
## BSBS21C -0.856 0.017 -50.202 0.000
## BSBS21D 0.826 0.013 61.540 0.000
## BSBS21E 1.085 0.013 86.451 0.000
## BSBS21F 1.086 0.014 77.499 0.000
## BSBS21G 0.644 0.013 48.221 0.000
## BSBS21H 0.533 0.014 36.916 0.000
## BSBS21I 1.142 0.015 76.326 0.000
## confident =~
## BSBS23A 1.000
## BSBS23B -0.978 0.023 -42.491 0.000
## BSBS23C -1.184 0.025 -47.965 0.000
## BSBS23D 1.128 0.021 54.805 0.000
## BSBS23E 1.147 0.022 52.555 0.000
## BSBS23F 0.917 0.024 38.057 0.000
## BSBS23G -0.944 0.023 -40.662 0.000
## BSBS23H -1.038 0.024 -43.472 0.000
## value =~
## BSBS24A 1.000
## BSBS24B 1.026 0.022 47.233 0.000
## BSBS24C 1.070 0.020 54.045 0.000
## BSBS24D 1.198 0.022 54.044 0.000
## BSBS24E 1.163 0.024 48.484 0.000
## BSBS24F 1.056 0.020 53.968 0.000
## BSBS24G 1.004 0.019 53.026 0.000
## BSBS24H 0.786 0.018 42.760 0.000
## BSBS24I 0.856 0.017 50.723 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## like_learning ~~
## confident 0.366 0.012 31.412 0.000
## value 0.339 0.012 28.557 0.000
## confident ~~
## value 0.227 0.009 24.941 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A 1.850 0.015 127.107 0.000
## .BSBS21B 2.761 0.017 164.192 0.000
## .BSBS21C 2.915 0.016 182.104 0.000
## .BSBS21D 1.673 0.014 123.129 0.000
## .BSBS21E 1.879 0.015 124.810 0.000
## .BSBS21F 2.072 0.016 130.895 0.000
## .BSBS21G 1.598 0.012 128.998 0.000
## .BSBS21H 1.507 0.012 120.613 0.000
## .BSBS21I 2.149 0.017 128.175 0.000
## .BSBS23A 1.799 0.013 143.102 0.000
## .BSBS23B 3.011 0.015 205.417 0.000
## .BSBS23C 2.794 0.016 174.212 0.000
## .BSBS23D 1.957 0.014 142.502 0.000
## .BSBS23E 2.136 0.014 147.983 0.000
## .BSBS23F 2.282 0.015 150.992 0.000
## .BSBS23G 3.105 0.015 211.372 0.000
## .BSBS23H 2.936 0.015 192.424 0.000
## .BSBS24A 1.851 0.014 131.525 0.000
## .BSBS24B 2.088 0.015 136.127 0.000
## .BSBS24C 1.792 0.014 125.283 0.000
## .BSBS24D 2.002 0.016 124.962 0.000
## .BSBS24E 2.273 0.017 133.654 0.000
## .BSBS24F 1.821 0.014 128.886 0.000
## .BSBS24G 1.707 0.014 125.205 0.000
## .BSBS24H 1.675 0.013 130.931 0.000
## .BSBS24I 1.574 0.012 130.544 0.000
## like_learning 0.000
## confident 0.000
## value 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A 0.184 0.005 36.527 0.000
## .BSBS21B 0.745 0.017 42.746 0.000
## .BSBS21C 0.520 0.012 41.850 0.000
## .BSBS21D 0.279 0.007 40.492 0.000
## .BSBS21E 0.130 0.004 31.767 0.000
## .BSBS21F 0.220 0.006 36.625 0.000
## .BSBS21G 0.326 0.008 42.026 0.000
## .BSBS21H 0.419 0.010 42.799 0.000
## .BSBS21I 0.259 0.007 37.052 0.000
## .BSBS23A 0.227 0.006 36.744 0.000
## .BSBS23B 0.460 0.011 40.427 0.000
## .BSBS23C 0.455 0.012 38.846 0.000
## .BSBS23D 0.242 0.007 35.374 0.000
## .BSBS23E 0.301 0.008 36.797 0.000
## .BSBS23F 0.556 0.013 41.311 0.000
## .BSBS23G 0.489 0.012 40.824 0.000
## .BSBS23H 0.484 0.012 40.190 0.000
## .BSBS24A 0.306 0.008 39.161 0.000
## .BSBS24B 0.424 0.011 40.254 0.000
## .BSBS24C 0.266 0.007 37.725 0.000
## .BSBS24D 0.334 0.009 37.726 0.000
## .BSBS24E 0.495 0.012 39.909 0.000
## .BSBS24F 0.261 0.007 37.765 0.000
## .BSBS24G 0.256 0.007 38.231 0.000
## .BSBS24H 0.347 0.008 41.223 0.000
## .BSBS24I 0.225 0.006 39.180 0.000
## like_learning 0.624 0.018 34.238 0.000
## confident 0.376 0.013 28.429 0.000
## value 0.450 0.016 27.773 0.000(Weak/metric invariance)
Test statistic = 16800.234 Degrees of freedom = 615 pvalue = 0.000 CFI = 0.887 TLI = 0.880 RMSEA = 0.082 AIC = 401487.992 BIC = 402014.157 SRMR = 0.061
estimate coefficients in both groups are equal, intercept estimates differ; anova is done below
science_cfa_2 <- cfa(model_cfa, data=dat1, group="gender", group.equal=c("loadings"))
summary(science_cfa_2,fit.measures=TRUE)## lavaan 0.6-6 ended normally after 50 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 162
## Number of equality constraints 23
##
## Number of observations per group:
## Girl 3995
## Boy 3815
##
## Model Test User Model:
##
## Test statistic 16800.234
## Degrees of freedom 615
## P-value (Chi-square) 0.000
## Test statistic for each group:
## Girl 8091.899
## Boy 8708.335
##
## Model Test Baseline Model:
##
## Test statistic 143641.597
## Degrees of freedom 650
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.887
## Tucker-Lewis Index (TLI) 0.880
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -200604.996
## Loglikelihood unrestricted model (H1) -192204.879
##
## Akaike (AIC) 401487.992
## Bayesian (BIC) 402455.871
## Sample-size adjusted Bayesian (BIC) 402014.157
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.082
## 90 Percent confidence interval - lower 0.081
## 90 Percent confidence interval - upper 0.083
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.061
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [Girl]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## like_learning =~
## BSBS21A 1.000
## BSBS21B (.p2.) -0.794 0.013 -61.682 0.000
## BSBS21C (.p3.) -0.879 0.011 -76.745 0.000
## BSBS21D (.p4.) 0.788 0.009 84.011 0.000
## BSBS21E (.p5.) 1.080 0.009 123.392 0.000
## BSBS21F (.p6.) 1.087 0.010 111.884 0.000
## BSBS21G (.p7.) 0.591 0.009 62.922 0.000
## BSBS21H (.p8.) 0.516 0.010 49.623 0.000
## BSBS21I (.p9.) 1.150 0.011 108.388 0.000
## confident =~
## BSBS23A 1.000
## BSBS23B (.11.) -1.061 0.017 -64.077 0.000
## BSBS23C (.12.) -1.283 0.018 -72.147 0.000
## BSBS23D (.13.) 1.153 0.015 75.693 0.000
## BSBS23E (.14.) 1.153 0.016 71.186 0.000
## BSBS23F (.15.) 0.924 0.017 53.330 0.000
## BSBS23G (.16.) -1.063 0.017 -63.660 0.000
## BSBS23H (.17.) -1.129 0.017 -64.648 0.000
## value =~
## BSBS24A 1.000
## BSBS24B (.19.) 1.045 0.016 64.624 0.000
## BSBS24C (.20.) 1.139 0.015 75.767 0.000
## BSBS24D (.21.) 1.270 0.017 75.131 0.000
## BSBS24E (.22.) 1.249 0.018 67.863 0.000
## BSBS24F (.23.) 1.075 0.015 71.815 0.000
## BSBS24G (.24.) 1.065 0.014 74.012 0.000
## BSBS24H (.25.) 0.789 0.013 58.564 0.000
## BSBS24I (.26.) 0.831 0.012 67.714 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## like_learning ~~
## confident 0.339 0.010 33.416 0.000
## value 0.284 0.010 28.584 0.000
## confident ~~
## value 0.178 0.007 24.049 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A 1.973 0.014 141.746 0.000
## .BSBS21B 2.766 0.015 179.542 0.000
## .BSBS21C 2.845 0.015 191.873 0.000
## .BSBS21D 1.718 0.013 132.722 0.000
## .BSBS21E 1.989 0.015 137.148 0.000
## .BSBS21F 2.207 0.015 145.387 0.000
## .BSBS21G 1.617 0.012 136.582 0.000
## .BSBS21H 1.581 0.013 125.133 0.000
## .BSBS21I 2.387 0.016 144.956 0.000
## .BSBS23A 1.840 0.012 153.413 0.000
## .BSBS23B 2.962 0.014 213.319 0.000
## .BSBS23C 2.686 0.015 177.255 0.000
## .BSBS23D 2.149 0.013 160.881 0.000
## .BSBS23E 2.434 0.014 171.709 0.000
## .BSBS23F 2.436 0.014 170.635 0.000
## .BSBS23G 3.022 0.014 217.448 0.000
## .BSBS23H 2.805 0.015 189.509 0.000
## .BSBS24A 1.865 0.013 139.906 0.000
## .BSBS24B 2.163 0.015 147.424 0.000
## .BSBS24C 1.774 0.014 128.445 0.000
## .BSBS24D 1.971 0.016 126.181 0.000
## .BSBS24E 2.330 0.017 137.742 0.000
## .BSBS24F 1.886 0.014 133.892 0.000
## .BSBS24G 1.718 0.013 130.062 0.000
## .BSBS24H 1.605 0.012 133.487 0.000
## .BSBS24I 1.505 0.011 135.202 0.000
## like_learning 0.000
## confident 0.000
## value 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A 0.171 0.005 36.935 0.000
## .BSBS21B 0.568 0.013 43.241 0.000
## .BSBS21C 0.412 0.010 42.238 0.000
## .BSBS21D 0.295 0.007 41.940 0.000
## .BSBS21E 0.136 0.004 33.359 0.000
## .BSBS21F 0.208 0.006 37.182 0.000
## .BSBS21G 0.349 0.008 43.392 0.000
## .BSBS21H 0.477 0.011 43.967 0.000
## .BSBS21I 0.286 0.007 38.610 0.000
## .BSBS23A 0.225 0.006 38.717 0.000
## .BSBS23B 0.376 0.009 40.674 0.000
## .BSBS23C 0.342 0.009 38.202 0.000
## .BSBS23D 0.248 0.007 37.490 0.000
## .BSBS23E 0.338 0.009 39.430 0.000
## .BSBS23F 0.516 0.012 42.479 0.000
## .BSBS23G 0.376 0.009 40.656 0.000
## .BSBS23H 0.429 0.011 40.708 0.000
## .BSBS24A 0.313 0.008 40.510 0.000
## .BSBS24B 0.427 0.010 41.351 0.000
## .BSBS24C 0.246 0.007 37.768 0.000
## .BSBS24D 0.334 0.009 38.365 0.000
## .BSBS24E 0.524 0.013 40.804 0.000
## .BSBS24F 0.333 0.008 40.171 0.000
## .BSBS24G 0.246 0.006 38.638 0.000
## .BSBS24H 0.330 0.008 42.231 0.000
## .BSBS24I 0.220 0.005 40.596 0.000
## like_learning 0.603 0.016 38.263 0.000
## confident 0.350 0.011 32.803 0.000
## value 0.397 0.012 32.174 0.000
##
##
## Group 2 [Boy]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## like_learning =~
## BSBS21A 1.000
## BSBS21B (.p2.) -0.794 0.013 -61.682 0.000
## BSBS21C (.p3.) -0.879 0.011 -76.745 0.000
## BSBS21D (.p4.) 0.788 0.009 84.011 0.000
## BSBS21E (.p5.) 1.080 0.009 123.392 0.000
## BSBS21F (.p6.) 1.087 0.010 111.884 0.000
## BSBS21G (.p7.) 0.591 0.009 62.922 0.000
## BSBS21H (.p8.) 0.516 0.010 49.623 0.000
## BSBS21I (.p9.) 1.150 0.011 108.388 0.000
## confident =~
## BSBS23A 1.000
## BSBS23B (.11.) -1.061 0.017 -64.077 0.000
## BSBS23C (.12.) -1.283 0.018 -72.147 0.000
## BSBS23D (.13.) 1.153 0.015 75.693 0.000
## BSBS23E (.14.) 1.153 0.016 71.186 0.000
## BSBS23F (.15.) 0.924 0.017 53.330 0.000
## BSBS23G (.16.) -1.063 0.017 -63.660 0.000
## BSBS23H (.17.) -1.129 0.017 -64.648 0.000
## value =~
## BSBS24A 1.000
## BSBS24B (.19.) 1.045 0.016 64.624 0.000
## BSBS24C (.20.) 1.139 0.015 75.767 0.000
## BSBS24D (.21.) 1.270 0.017 75.131 0.000
## BSBS24E (.22.) 1.249 0.018 67.863 0.000
## BSBS24F (.23.) 1.075 0.015 71.815 0.000
## BSBS24G (.24.) 1.065 0.014 74.012 0.000
## BSBS24H (.25.) 0.789 0.013 58.564 0.000
## BSBS24I (.26.) 0.831 0.012 67.714 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## like_learning ~~
## confident 0.350 0.011 33.050 0.000
## value 0.328 0.011 29.911 0.000
## confident ~~
## value 0.207 0.008 25.902 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A 1.850 0.015 126.737 0.000
## .BSBS21B 2.761 0.017 159.738 0.000
## .BSBS21C 2.915 0.016 179.780 0.000
## .BSBS21D 1.673 0.013 125.966 0.000
## .BSBS21E 1.879 0.015 124.865 0.000
## .BSBS21F 2.072 0.016 130.509 0.000
## .BSBS21G 1.598 0.012 133.037 0.000
## .BSBS21H 1.507 0.012 121.441 0.000
## .BSBS21I 2.149 0.017 127.276 0.000
## .BSBS23A 1.799 0.012 145.866 0.000
## .BSBS23B 3.011 0.015 203.528 0.000
## .BSBS23C 2.794 0.016 172.101 0.000
## .BSBS23D 1.957 0.014 143.332 0.000
## .BSBS23E 2.136 0.014 150.049 0.000
## .BSBS23F 2.282 0.015 151.923 0.000
## .BSBS23G 3.105 0.015 206.519 0.000
## .BSBS23H 2.936 0.015 190.197 0.000
## .BSBS24A 1.851 0.014 133.790 0.000
## .BSBS24B 2.088 0.015 137.107 0.000
## .BSBS24C 1.792 0.015 123.218 0.000
## .BSBS24D 2.002 0.016 123.445 0.000
## .BSBS24E 2.273 0.017 131.287 0.000
## .BSBS24F 1.821 0.014 129.978 0.000
## .BSBS24G 1.707 0.014 123.265 0.000
## .BSBS24H 1.675 0.013 132.338 0.000
## .BSBS24I 1.574 0.012 134.744 0.000
## like_learning 0.000
## confident 0.000
## value 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A 0.184 0.005 36.633 0.000
## .BSBS21B 0.743 0.017 42.594 0.000
## .BSBS21C 0.517 0.012 41.769 0.000
## .BSBS21D 0.283 0.007 40.859 0.000
## .BSBS21E 0.130 0.004 32.039 0.000
## .BSBS21F 0.220 0.006 36.707 0.000
## .BSBS21G 0.331 0.008 42.327 0.000
## .BSBS21H 0.420 0.010 42.865 0.000
## .BSBS21I 0.257 0.007 37.005 0.000
## .BSBS23A 0.235 0.006 37.740 0.000
## .BSBS23B 0.446 0.011 40.174 0.000
## .BSBS23C 0.438 0.011 38.454 0.000
## .BSBS23D 0.253 0.007 36.320 0.000
## .BSBS23E 0.315 0.008 37.773 0.000
## .BSBS23F 0.566 0.014 41.584 0.000
## .BSBS23G 0.472 0.012 40.363 0.000
## .BSBS23H 0.469 0.012 39.897 0.000
## .BSBS24A 0.310 0.008 39.651 0.000
## .BSBS24B 0.426 0.011 40.483 0.000
## .BSBS24C 0.262 0.007 37.481 0.000
## .BSBS24D 0.326 0.009 37.481 0.000
## .BSBS24E 0.489 0.012 39.689 0.000
## .BSBS24F 0.263 0.007 38.169 0.000
## .BSBS24G 0.255 0.007 38.118 0.000
## .BSBS24H 0.350 0.008 41.462 0.000
## .BSBS24I 0.231 0.006 39.951 0.000
## like_learning 0.629 0.017 37.501 0.000
## confident 0.345 0.011 32.190 0.000
## value 0.420 0.013 31.813 0.000anova(science_cfa_1, science_cfa_2)(Strong/scalar invariance)
Test statistic = 17369.024 Degrees of freedom = 638 pvalue = 0.000 CFI = 0.883 TLI = 0.881 RMSEA = 0.082 AIC = 402010.782 BIC = 402449.884 SRMR = 0.061
now loading and intercepts are the same in both groups. anova is below.
science_cfa_3 <- cfa(model_cfa, data=dat1, group="gender", group.equal=c("loadings", "intercepts"))
summary(science_cfa_3, fit.measures=TRUE)## lavaan 0.6-6 ended normally after 77 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 165
## Number of equality constraints 49
##
## Number of observations per group:
## Girl 3995
## Boy 3815
##
## Model Test User Model:
##
## Test statistic 17369.024
## Degrees of freedom 638
## P-value (Chi-square) 0.000
## Test statistic for each group:
## Girl 8372.349
## Boy 8996.675
##
## Model Test Baseline Model:
##
## Test statistic 143641.597
## Degrees of freedom 650
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.883
## Tucker-Lewis Index (TLI) 0.881
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -200889.391
## Loglikelihood unrestricted model (H1) -192204.879
##
## Akaike (AIC) 402010.782
## Bayesian (BIC) 402818.509
## Sample-size adjusted Bayesian (BIC) 402449.884
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.082
## 90 Percent confidence interval - lower 0.081
## 90 Percent confidence interval - upper 0.083
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.061
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [Girl]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## like_learning =~
## BSBS21A 1.000
## BSBS21B (.p2.) -0.789 0.013 -61.429 0.000
## BSBS21C (.p3.) -0.877 0.011 -76.834 0.000
## BSBS21D (.p4.) 0.785 0.009 84.014 0.000
## BSBS21E (.p5.) 1.079 0.009 123.762 0.000
## BSBS21F (.p6.) 1.087 0.010 112.278 0.000
## BSBS21G (.p7.) 0.588 0.009 62.826 0.000
## BSBS21H (.p8.) 0.517 0.010 49.818 0.000
## BSBS21I (.p9.) 1.154 0.011 108.641 0.000
## confident =~
## BSBS23A 1.000
## BSBS23B (.11.) -1.062 0.017 -63.660 0.000
## BSBS23C (.12.) -1.289 0.018 -71.852 0.000
## BSBS23D (.13.) 1.168 0.015 75.711 0.000
## BSBS23E (.14.) 1.177 0.017 71.231 0.000
## BSBS23F (.15.) 0.937 0.017 53.615 0.000
## BSBS23G (.16.) -1.067 0.017 -63.450 0.000
## BSBS23H (.17.) -1.138 0.018 -64.645 0.000
## value =~
## BSBS24A 1.000
## BSBS24B (.19.) 1.045 0.016 64.545 0.000
## BSBS24C (.20.) 1.139 0.015 75.757 0.000
## BSBS24D (.21.) 1.270 0.017 75.122 0.000
## BSBS24E (.22.) 1.249 0.018 67.838 0.000
## BSBS24F (.23.) 1.075 0.015 71.725 0.000
## BSBS24G (.24.) 1.065 0.014 73.994 0.000
## BSBS24H (.25.) 0.789 0.013 58.454 0.000
## BSBS24I (.26.) 0.830 0.012 67.563 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## like_learning ~~
## confident 0.336 0.010 33.399 0.000
## value 0.284 0.010 28.582 0.000
## confident ~~
## value 0.177 0.007 24.042 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A (.59.) 1.970 0.013 147.858 0.000
## .BSBS21B (.60.) 2.725 0.013 203.826 0.000
## .BSBS21C (.61.) 2.831 0.013 212.505 0.000
## .BSBS21D (.62.) 1.741 0.012 151.014 0.000
## .BSBS21E (.63.) 1.997 0.014 141.956 0.000
## .BSBS21F (.64.) 2.203 0.015 151.930 0.000
## .BSBS21G (.65.) 1.642 0.010 166.213 0.000
## .BSBS21H (.66.) 1.574 0.010 158.070 0.000
## .BSBS21I (.67.) 2.334 0.016 149.944 0.000
## .BSBS23A (.68.) 1.878 0.011 171.272 0.000
## .BSBS23B (.69.) 2.926 0.012 235.684 0.000
## .BSBS23C (.70.) 2.666 0.014 189.387 0.000
## .BSBS23D (.71.) 2.125 0.012 170.340 0.000
## .BSBS23E (.72.) 2.356 0.013 181.392 0.000
## .BSBS23F (.73.) 2.418 0.012 198.277 0.000
## .BSBS23G (.74.) 3.002 0.012 240.299 0.000
## .BSBS23H (.75.) 2.801 0.013 212.016 0.000
## .BSBS24A (.76.) 1.859 0.012 155.315 0.000
## .BSBS24B (.77.) 2.127 0.013 164.336 0.000
## .BSBS24C (.78.) 1.783 0.013 138.283 0.000
## .BSBS24D (.79.) 1.987 0.014 137.421 0.000
## .BSBS24E (.80.) 2.302 0.015 152.978 0.000
## .BSBS24F (.81.) 1.851 0.013 147.067 0.000
## .BSBS24G (.82.) 1.713 0.012 140.298 0.000
## .BSBS24H (.83.) 1.639 0.010 157.856 0.000
## .BSBS24I (.84.) 1.538 0.010 153.714 0.000
## lk_lrnn 0.000
## confdnt 0.000
## value 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A 0.171 0.005 36.909 0.000
## .BSBS21B 0.570 0.013 43.262 0.000
## .BSBS21C 0.413 0.010 42.246 0.000
## .BSBS21D 0.296 0.007 41.958 0.000
## .BSBS21E 0.136 0.004 33.357 0.000
## .BSBS21F 0.208 0.006 37.159 0.000
## .BSBS21G 0.350 0.008 43.403 0.000
## .BSBS21H 0.477 0.011 43.964 0.000
## .BSBS21I 0.290 0.007 38.618 0.000
## .BSBS23A 0.227 0.006 38.845 0.000
## .BSBS23B 0.379 0.009 40.746 0.000
## .BSBS23C 0.343 0.009 38.250 0.000
## .BSBS23D 0.248 0.007 37.383 0.000
## .BSBS23E 0.344 0.009 39.372 0.000
## .BSBS23F 0.516 0.012 42.446 0.000
## .BSBS23G 0.377 0.009 40.685 0.000
## .BSBS23H 0.429 0.011 40.689 0.000
## .BSBS24A 0.313 0.008 40.505 0.000
## .BSBS24B 0.428 0.010 41.358 0.000
## .BSBS24C 0.246 0.007 37.751 0.000
## .BSBS24D 0.334 0.009 38.350 0.000
## .BSBS24E 0.524 0.013 40.800 0.000
## .BSBS24F 0.335 0.008 40.186 0.000
## .BSBS24G 0.246 0.006 38.629 0.000
## .BSBS24H 0.332 0.008 42.240 0.000
## .BSBS24I 0.222 0.005 40.621 0.000
## like_learning 0.604 0.016 38.288 0.000
## confident 0.344 0.011 32.683 0.000
## value 0.397 0.012 32.169 0.000
##
##
## Group 2 [Boy]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## like_learning =~
## BSBS21A 1.000
## BSBS21B (.p2.) -0.789 0.013 -61.429 0.000
## BSBS21C (.p3.) -0.877 0.011 -76.834 0.000
## BSBS21D (.p4.) 0.785 0.009 84.014 0.000
## BSBS21E (.p5.) 1.079 0.009 123.762 0.000
## BSBS21F (.p6.) 1.087 0.010 112.278 0.000
## BSBS21G (.p7.) 0.588 0.009 62.826 0.000
## BSBS21H (.p8.) 0.517 0.010 49.818 0.000
## BSBS21I (.p9.) 1.154 0.011 108.641 0.000
## confident =~
## BSBS23A 1.000
## BSBS23B (.11.) -1.062 0.017 -63.660 0.000
## BSBS23C (.12.) -1.289 0.018 -71.852 0.000
## BSBS23D (.13.) 1.168 0.015 75.711 0.000
## BSBS23E (.14.) 1.177 0.017 71.231 0.000
## BSBS23F (.15.) 0.937 0.017 53.615 0.000
## BSBS23G (.16.) -1.067 0.017 -63.450 0.000
## BSBS23H (.17.) -1.138 0.018 -64.645 0.000
## value =~
## BSBS24A 1.000
## BSBS24B (.19.) 1.045 0.016 64.545 0.000
## BSBS24C (.20.) 1.139 0.015 75.757 0.000
## BSBS24D (.21.) 1.270 0.017 75.122 0.000
## BSBS24E (.22.) 1.249 0.018 67.838 0.000
## BSBS24F (.23.) 1.075 0.015 71.725 0.000
## BSBS24G (.24.) 1.065 0.014 73.994 0.000
## BSBS24H (.25.) 0.789 0.013 58.454 0.000
## BSBS24I (.26.) 0.830 0.012 67.563 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## like_learning ~~
## confident 0.347 0.011 33.031 0.000
## value 0.328 0.011 29.911 0.000
## confident ~~
## value 0.206 0.008 25.894 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A (.59.) 1.970 0.013 147.858 0.000
## .BSBS21B (.60.) 2.725 0.013 203.826 0.000
## .BSBS21C (.61.) 2.831 0.013 212.505 0.000
## .BSBS21D (.62.) 1.741 0.012 151.014 0.000
## .BSBS21E (.63.) 1.997 0.014 141.956 0.000
## .BSBS21F (.64.) 2.203 0.015 151.930 0.000
## .BSBS21G (.65.) 1.642 0.010 166.213 0.000
## .BSBS21H (.66.) 1.574 0.010 158.070 0.000
## .BSBS21I (.67.) 2.334 0.016 149.944 0.000
## .BSBS23A (.68.) 1.878 0.011 171.272 0.000
## .BSBS23B (.69.) 2.926 0.012 235.684 0.000
## .BSBS23C (.70.) 2.666 0.014 189.387 0.000
## .BSBS23D (.71.) 2.125 0.012 170.340 0.000
## .BSBS23E (.72.) 2.356 0.013 181.392 0.000
## .BSBS23F (.73.) 2.418 0.012 198.277 0.000
## .BSBS23G (.74.) 3.002 0.012 240.299 0.000
## .BSBS23H (.75.) 2.801 0.013 212.016 0.000
## .BSBS24A (.76.) 1.859 0.012 155.315 0.000
## .BSBS24B (.77.) 2.127 0.013 164.336 0.000
## .BSBS24C (.78.) 1.783 0.013 138.283 0.000
## .BSBS24D (.79.) 1.987 0.014 137.421 0.000
## .BSBS24E (.80.) 2.302 0.015 152.978 0.000
## .BSBS24F (.81.) 1.851 0.013 147.067 0.000
## .BSBS24G (.82.) 1.713 0.012 140.298 0.000
## .BSBS24H (.83.) 1.639 0.010 157.856 0.000
## .BSBS24I (.84.) 1.538 0.010 153.714 0.000
## lk_lrnn -0.117 0.018 -6.407 0.000
## confdnt -0.122 0.014 -8.734 0.000
## value -0.001 0.015 -0.080 0.936
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A 0.184 0.005 36.608 0.000
## .BSBS21B 0.746 0.018 42.610 0.000
## .BSBS21C 0.518 0.012 41.774 0.000
## .BSBS21D 0.284 0.007 40.879 0.000
## .BSBS21E 0.130 0.004 32.037 0.000
## .BSBS21F 0.219 0.006 36.686 0.000
## .BSBS21G 0.332 0.008 42.339 0.000
## .BSBS21H 0.420 0.010 42.862 0.000
## .BSBS21I 0.260 0.007 37.017 0.000
## .BSBS23A 0.238 0.006 37.888 0.000
## .BSBS23B 0.449 0.011 40.240 0.000
## .BSBS23C 0.440 0.011 38.497 0.000
## .BSBS23D 0.253 0.007 36.217 0.000
## .BSBS23E 0.320 0.008 37.704 0.000
## .BSBS23F 0.566 0.014 41.555 0.000
## .BSBS23G 0.474 0.012 40.389 0.000
## .BSBS23H 0.469 0.012 39.886 0.000
## .BSBS24A 0.310 0.008 39.644 0.000
## .BSBS24B 0.428 0.011 40.489 0.000
## .BSBS24C 0.262 0.007 37.467 0.000
## .BSBS24D 0.326 0.009 37.467 0.000
## .BSBS24E 0.489 0.012 39.685 0.000
## .BSBS24F 0.265 0.007 38.183 0.000
## .BSBS24G 0.255 0.007 38.109 0.000
## .BSBS24H 0.352 0.008 41.471 0.000
## .BSBS24I 0.233 0.006 39.976 0.000
## like_learning 0.629 0.017 37.525 0.000
## confident 0.339 0.011 32.066 0.000
## value 0.420 0.013 31.808 0.000modindices(science_cfa_3)And… well, here i have literally no idea how to search for the items, which have intercept estimates that are non-invariant across groups. Because the output gives 760 rows are I’m kinda scared -
anova(science_cfa_2, science_cfa_3)Test statistic = 17381.952 Degrees of freedom = 664 pvalue = 0.000 CFI = 0.881 TLI = 0.883 RMSEA = 0.081 AIC = 402271.710 BIC = 402612.393 SRMR = 0.061
Loading, intercepts, variences are equal in both groups
science_cfa_4 <- cfa(model_cfa, data=dat1, group="gender", group.equal=c("loadings", "intercepts", "residuals"))
summary(science_cfa_4, fit.measures=TRUE)## lavaan 0.6-6 ended normally after 79 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 165
## Number of equality constraints 75
##
## Number of observations per group:
## Girl 3995
## Boy 3815
##
## Model Test User Model:
##
## Test statistic 17681.952
## Degrees of freedom 664
## P-value (Chi-square) 0.000
## Test statistic for each group:
## Girl 8531.434
## Boy 9150.519
##
## Model Test Baseline Model:
##
## Test statistic 143641.597
## Degrees of freedom 650
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.881
## Tucker-Lewis Index (TLI) 0.883
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -201045.855
## Loglikelihood unrestricted model (H1) -192204.879
##
## Akaike (AIC) 402271.710
## Bayesian (BIC) 402898.395
## Sample-size adjusted Bayesian (BIC) 402612.393
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.081
## 90 Percent confidence interval - lower 0.080
## 90 Percent confidence interval - upper 0.082
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.061
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [Girl]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## like_learning =~
## BSBS21A 1.000
## BSBS21B (.p2.) -0.782 0.013 -60.527 0.000
## BSBS21C (.p3.) -0.875 0.011 -76.350 0.000
## BSBS21D (.p4.) 0.785 0.009 83.870 0.000
## BSBS21E (.p5.) 1.080 0.009 123.630 0.000
## BSBS21F (.p6.) 1.087 0.010 112.239 0.000
## BSBS21G (.p7.) 0.587 0.009 62.628 0.000
## BSBS21H (.p8.) 0.516 0.010 49.611 0.000
## BSBS21I (.p9.) 1.155 0.011 108.539 0.000
## confident =~
## BSBS23A 1.000
## BSBS23B (.11.) -1.063 0.017 -63.491 0.000
## BSBS23C (.12.) -1.289 0.018 -71.508 0.000
## BSBS23D (.13.) 1.168 0.015 75.408 0.000
## BSBS23E (.14.) 1.175 0.017 70.955 0.000
## BSBS23F (.15.) 0.936 0.018 53.395 0.000
## BSBS23G (.16.) -1.065 0.017 -63.053 0.000
## BSBS23H (.17.) -1.141 0.018 -64.643 0.000
## value =~
## BSBS24A 1.000
## BSBS24B (.19.) 1.045 0.016 64.563 0.000
## BSBS24C (.20.) 1.138 0.015 75.730 0.000
## BSBS24D (.21.) 1.270 0.017 75.087 0.000
## BSBS24E (.22.) 1.250 0.018 67.839 0.000
## BSBS24F (.23.) 1.073 0.015 71.416 0.000
## BSBS24G (.24.) 1.065 0.014 73.971 0.000
## BSBS24H (.25.) 0.789 0.013 58.500 0.000
## BSBS24I (.26.) 0.831 0.012 67.618 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## like_learning ~~
## confident 0.336 0.010 33.417 0.000
## value 0.285 0.010 28.637 0.000
## confident ~~
## value 0.178 0.007 24.179 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A (.59.) 1.970 0.013 147.756 0.000
## .BSBS21B (.60.) 2.719 0.013 203.130 0.000
## .BSBS21C (.61.) 2.829 0.013 211.887 0.000
## .BSBS21D (.62.) 1.741 0.012 151.138 0.000
## .BSBS21E (.63.) 1.997 0.014 142.037 0.000
## .BSBS21F (.64.) 2.203 0.015 151.836 0.000
## .BSBS21G (.65.) 1.641 0.010 166.413 0.000
## .BSBS21H (.66.) 1.575 0.010 158.186 0.000
## .BSBS21I (.67.) 2.337 0.016 150.224 0.000
## .BSBS23A (.68.) 1.879 0.011 171.536 0.000
## .BSBS23B (.69.) 2.923 0.012 234.939 0.000
## .BSBS23C (.70.) 2.663 0.014 188.555 0.000
## .BSBS23D (.71.) 2.124 0.012 170.689 0.000
## .BSBS23E (.72.) 2.358 0.013 182.387 0.000
## .BSBS23F (.73.) 2.417 0.012 198.125 0.000
## .BSBS23G (.74.) 2.999 0.013 239.700 0.000
## .BSBS23H (.75.) 2.801 0.013 211.926 0.000
## .BSBS24A (.76.) 1.859 0.012 155.312 0.000
## .BSBS24B (.77.) 2.127 0.013 164.297 0.000
## .BSBS24C (.78.) 1.783 0.013 138.224 0.000
## .BSBS24D (.79.) 1.987 0.014 137.424 0.000
## .BSBS24E (.80.) 2.303 0.015 153.012 0.000
## .BSBS24F (.81.) 1.855 0.013 147.814 0.000
## .BSBS24G (.82.) 1.713 0.012 140.237 0.000
## .BSBS24H (.83.) 1.640 0.010 157.721 0.000
## .BSBS24I (.84.) 1.539 0.010 153.507 0.000
## lk_lrnn 0.000
## confdnt 0.000
## value 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A (.27.) 0.177 0.003 51.732 0.000
## .BSBS21B (.28.) 0.657 0.011 60.742 0.000
## .BSBS21C (.29.) 0.464 0.008 59.386 0.000
## .BSBS21D (.30.) 0.290 0.005 58.486 0.000
## .BSBS21E (.31.) 0.134 0.003 45.814 0.000
## .BSBS21F (.32.) 0.213 0.004 51.915 0.000
## .BSBS21G (.33.) 0.341 0.006 60.595 0.000
## .BSBS21H (.34.) 0.449 0.007 61.380 0.000
## .BSBS21I (.35.) 0.275 0.005 53.250 0.000
## .BSBS23A (.36.) 0.233 0.004 53.910 0.000
## .BSBS23B (.37.) 0.412 0.007 57.007 0.000
## .BSBS23C (.38.) 0.388 0.007 53.925 0.000
## .BSBS23D (.39.) 0.251 0.005 51.617 0.000
## .BSBS23E (.40.) 0.334 0.006 54.197 0.000
## .BSBS23F (.41.) 0.541 0.009 59.267 0.000
## .BSBS23G (.42.) 0.423 0.007 57.134 0.000
## .BSBS23H (.43.) 0.446 0.008 56.657 0.000
## .BSBS24A (.44.) 0.311 0.006 56.454 0.000
## .BSBS24B (.45.) 0.428 0.007 57.698 0.000
## .BSBS24C (.46.) 0.254 0.005 52.869 0.000
## .BSBS24D (.47.) 0.331 0.006 53.295 0.000
## .BSBS24E (.48.) 0.507 0.009 56.696 0.000
## .BSBS24F (.49.) 0.301 0.005 55.280 0.000
## .BSBS24G (.50.) 0.251 0.005 53.972 0.000
## .BSBS24H (.51.) 0.341 0.006 59.066 0.000
## .BSBS24I (.52.) 0.227 0.004 56.772 0.000
## lk_lrnn 0.603 0.016 38.220 0.000
## confdnt 0.341 0.010 32.579 0.000
## value 0.398 0.012 32.179 0.000
##
##
## Group 2 [Boy]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## like_learning =~
## BSBS21A 1.000
## BSBS21B (.p2.) -0.782 0.013 -60.527 0.000
## BSBS21C (.p3.) -0.875 0.011 -76.350 0.000
## BSBS21D (.p4.) 0.785 0.009 83.870 0.000
## BSBS21E (.p5.) 1.080 0.009 123.630 0.000
## BSBS21F (.p6.) 1.087 0.010 112.239 0.000
## BSBS21G (.p7.) 0.587 0.009 62.628 0.000
## BSBS21H (.p8.) 0.516 0.010 49.611 0.000
## BSBS21I (.p9.) 1.155 0.011 108.539 0.000
## confident =~
## BSBS23A 1.000
## BSBS23B (.11.) -1.063 0.017 -63.491 0.000
## BSBS23C (.12.) -1.289 0.018 -71.508 0.000
## BSBS23D (.13.) 1.168 0.015 75.408 0.000
## BSBS23E (.14.) 1.175 0.017 70.955 0.000
## BSBS23F (.15.) 0.936 0.018 53.395 0.000
## BSBS23G (.16.) -1.065 0.017 -63.053 0.000
## BSBS23H (.17.) -1.141 0.018 -64.643 0.000
## value =~
## BSBS24A 1.000
## BSBS24B (.19.) 1.045 0.016 64.563 0.000
## BSBS24C (.20.) 1.138 0.015 75.730 0.000
## BSBS24D (.21.) 1.270 0.017 75.087 0.000
## BSBS24E (.22.) 1.250 0.018 67.839 0.000
## BSBS24F (.23.) 1.073 0.015 71.416 0.000
## BSBS24G (.24.) 1.065 0.014 73.971 0.000
## BSBS24H (.25.) 0.789 0.013 58.500 0.000
## BSBS24I (.26.) 0.831 0.012 67.618 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## like_learning ~~
## confident 0.346 0.011 32.944 0.000
## value 0.327 0.011 29.884 0.000
## confident ~~
## value 0.204 0.008 25.709 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A (.59.) 1.970 0.013 147.756 0.000
## .BSBS21B (.60.) 2.719 0.013 203.130 0.000
## .BSBS21C (.61.) 2.829 0.013 211.887 0.000
## .BSBS21D (.62.) 1.741 0.012 151.138 0.000
## .BSBS21E (.63.) 1.997 0.014 142.037 0.000
## .BSBS21F (.64.) 2.203 0.015 151.836 0.000
## .BSBS21G (.65.) 1.641 0.010 166.413 0.000
## .BSBS21H (.66.) 1.575 0.010 158.186 0.000
## .BSBS21I (.67.) 2.337 0.016 150.224 0.000
## .BSBS23A (.68.) 1.879 0.011 171.536 0.000
## .BSBS23B (.69.) 2.923 0.012 234.939 0.000
## .BSBS23C (.70.) 2.663 0.014 188.555 0.000
## .BSBS23D (.71.) 2.124 0.012 170.689 0.000
## .BSBS23E (.72.) 2.358 0.013 182.387 0.000
## .BSBS23F (.73.) 2.417 0.012 198.125 0.000
## .BSBS23G (.74.) 2.999 0.013 239.700 0.000
## .BSBS23H (.75.) 2.801 0.013 211.926 0.000
## .BSBS24A (.76.) 1.859 0.012 155.312 0.000
## .BSBS24B (.77.) 2.127 0.013 164.297 0.000
## .BSBS24C (.78.) 1.783 0.013 138.224 0.000
## .BSBS24D (.79.) 1.987 0.014 137.424 0.000
## .BSBS24E (.80.) 2.303 0.015 153.012 0.000
## .BSBS24F (.81.) 1.855 0.013 147.814 0.000
## .BSBS24G (.82.) 1.713 0.012 140.237 0.000
## .BSBS24H (.83.) 1.640 0.010 157.721 0.000
## .BSBS24I (.84.) 1.539 0.010 153.507 0.000
## lk_lrnn -0.117 0.018 -6.411 0.000
## confdnt -0.122 0.014 -8.720 0.000
## value -0.001 0.015 -0.075 0.940
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A (.27.) 0.177 0.003 51.732 0.000
## .BSBS21B (.28.) 0.657 0.011 60.742 0.000
## .BSBS21C (.29.) 0.464 0.008 59.386 0.000
## .BSBS21D (.30.) 0.290 0.005 58.486 0.000
## .BSBS21E (.31.) 0.134 0.003 45.814 0.000
## .BSBS21F (.32.) 0.213 0.004 51.915 0.000
## .BSBS21G (.33.) 0.341 0.006 60.595 0.000
## .BSBS21H (.34.) 0.449 0.007 61.380 0.000
## .BSBS21I (.35.) 0.275 0.005 53.250 0.000
## .BSBS23A (.36.) 0.233 0.004 53.910 0.000
## .BSBS23B (.37.) 0.412 0.007 57.007 0.000
## .BSBS23C (.38.) 0.388 0.007 53.925 0.000
## .BSBS23D (.39.) 0.251 0.005 51.617 0.000
## .BSBS23E (.40.) 0.334 0.006 54.197 0.000
## .BSBS23F (.41.) 0.541 0.009 59.267 0.000
## .BSBS23G (.42.) 0.423 0.007 57.134 0.000
## .BSBS23H (.43.) 0.446 0.008 56.657 0.000
## .BSBS24A (.44.) 0.311 0.006 56.454 0.000
## .BSBS24B (.45.) 0.428 0.007 57.698 0.000
## .BSBS24C (.46.) 0.254 0.005 52.869 0.000
## .BSBS24D (.47.) 0.331 0.006 53.295 0.000
## .BSBS24E (.48.) 0.507 0.009 56.696 0.000
## .BSBS24F (.49.) 0.301 0.005 55.280 0.000
## .BSBS24G (.50.) 0.251 0.005 53.972 0.000
## .BSBS24H (.51.) 0.341 0.006 59.066 0.000
## .BSBS24I (.52.) 0.227 0.004 56.772 0.000
## lk_lrnn 0.629 0.017 37.573 0.000
## confdnt 0.341 0.011 32.087 0.000
## value 0.420 0.013 31.805 0.000anova(science_cfa_3, science_cfa_4)Test statistic = 17697.472 Degrees of freedom = 670 pvalue = 0.000 CFI = 0.881 TLI = 0.884 RMSEA = 0.081 AIC = 402275.230 BIC = 402593.200 SRMR = 0.063
Loading, intercepts, residuals + variences and covariences are equal.
science_cfa_5 <- cfa(model_cfa, data=dat1, group="gender", group.equal=c("loadings", "intercepts", "residuals", "lv.variances", "lv.covariances"))
summary(science_cfa_5, fit.measures=TRUE)## lavaan 0.6-6 ended normally after 79 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 165
## Number of equality constraints 81
##
## Number of observations per group:
## Girl 3995
## Boy 3815
##
## Model Test User Model:
##
## Test statistic 17697.472
## Degrees of freedom 670
## P-value (Chi-square) 0.000
## Test statistic for each group:
## Girl 8538.907
## Boy 9158.565
##
## Model Test Baseline Model:
##
## Test statistic 143641.597
## Degrees of freedom 650
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.881
## Tucker-Lewis Index (TLI) 0.884
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -201053.615
## Loglikelihood unrestricted model (H1) -192204.879
##
## Akaike (AIC) 402275.230
## Bayesian (BIC) 402860.135
## Sample-size adjusted Bayesian (BIC) 402593.200
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.081
## 90 Percent confidence interval - lower 0.080
## 90 Percent confidence interval - upper 0.082
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.063
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [Girl]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## like_learning =~
## BSBS21A 1.000
## BSBS21B (.p2.) -0.782 0.013 -60.527 0.000
## BSBS21C (.p3.) -0.875 0.011 -76.351 0.000
## BSBS21D (.p4.) 0.785 0.009 83.866 0.000
## BSBS21E (.p5.) 1.080 0.009 123.619 0.000
## BSBS21F (.p6.) 1.087 0.010 112.237 0.000
## BSBS21G (.p7.) 0.587 0.009 62.628 0.000
## BSBS21H (.p8.) 0.516 0.010 49.609 0.000
## BSBS21I (.p9.) 1.155 0.011 108.538 0.000
## confident =~
## BSBS23A 1.000
## BSBS23B (.11.) -1.063 0.017 -63.496 0.000
## BSBS23C (.12.) -1.289 0.018 -71.518 0.000
## BSBS23D (.13.) 1.167 0.015 75.405 0.000
## BSBS23E (.14.) 1.175 0.017 70.955 0.000
## BSBS23F (.15.) 0.936 0.018 53.397 0.000
## BSBS23G (.16.) -1.065 0.017 -63.056 0.000
## BSBS23H (.17.) -1.141 0.018 -64.646 0.000
## value =~
## BSBS24A 1.000
## BSBS24B (.19.) 1.045 0.016 64.564 0.000
## BSBS24C (.20.) 1.138 0.015 75.728 0.000
## BSBS24D (.21.) 1.270 0.017 75.088 0.000
## BSBS24E (.22.) 1.250 0.018 67.845 0.000
## BSBS24F (.23.) 1.073 0.015 71.420 0.000
## BSBS24G (.24.) 1.065 0.014 73.970 0.000
## BSBS24H (.25.) 0.789 0.013 58.499 0.000
## BSBS24I (.26.) 0.831 0.012 67.616 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## like_learning ~~
## confdnt (.56.) 0.341 0.008 44.211 0.000
## value (.57.) 0.306 0.008 39.320 0.000
## confident ~~
## value (.58.) 0.190 0.006 33.491 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A (.59.) 1.970 0.013 146.474 0.000
## .BSBS21B (.60.) 2.719 0.013 202.055 0.000
## .BSBS21C (.61.) 2.829 0.013 210.477 0.000
## .BSBS21D (.62.) 1.741 0.012 150.054 0.000
## .BSBS21E (.63.) 1.997 0.014 140.746 0.000
## .BSBS21F (.64.) 2.203 0.015 150.519 0.000
## .BSBS21G (.65.) 1.641 0.010 165.499 0.000
## .BSBS21H (.66.) 1.575 0.010 157.526 0.000
## .BSBS21I (.67.) 2.337 0.016 148.944 0.000
## .BSBS23A (.68.) 1.879 0.011 171.607 0.000
## .BSBS23B (.69.) 2.923 0.012 235.026 0.000
## .BSBS23C (.70.) 2.663 0.014 188.632 0.000
## .BSBS23D (.71.) 2.124 0.012 170.772 0.000
## .BSBS23E (.72.) 2.358 0.013 182.468 0.000
## .BSBS23F (.73.) 2.417 0.012 198.186 0.000
## .BSBS23G (.74.) 2.999 0.013 239.790 0.000
## .BSBS23H (.75.) 2.801 0.013 212.009 0.000
## .BSBS24A (.76.) 1.859 0.012 153.874 0.000
## .BSBS24B (.77.) 2.127 0.013 162.877 0.000
## .BSBS24C (.78.) 1.783 0.013 136.802 0.000
## .BSBS24D (.79.) 1.987 0.015 136.021 0.000
## .BSBS24E (.80.) 2.303 0.015 151.608 0.000
## .BSBS24F (.81.) 1.855 0.013 146.382 0.000
## .BSBS24G (.82.) 1.713 0.012 138.829 0.000
## .BSBS24H (.83.) 1.640 0.010 156.515 0.000
## .BSBS24I (.84.) 1.539 0.010 152.111 0.000
## lk_lrnn 0.000
## confdnt 0.000
## value 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A (.27.) 0.177 0.003 51.733 0.000
## .BSBS21B (.28.) 0.657 0.011 60.742 0.000
## .BSBS21C (.29.) 0.464 0.008 59.385 0.000
## .BSBS21D (.30.) 0.290 0.005 58.485 0.000
## .BSBS21E (.31.) 0.134 0.003 45.815 0.000
## .BSBS21F (.32.) 0.213 0.004 51.913 0.000
## .BSBS21G (.33.) 0.341 0.006 60.595 0.000
## .BSBS21H (.34.) 0.449 0.007 61.379 0.000
## .BSBS21I (.35.) 0.275 0.005 53.248 0.000
## .BSBS23A (.36.) 0.233 0.004 53.907 0.000
## .BSBS23B (.37.) 0.412 0.007 57.006 0.000
## .BSBS23C (.38.) 0.388 0.007 53.921 0.000
## .BSBS23D (.39.) 0.252 0.005 51.621 0.000
## .BSBS23E (.40.) 0.334 0.006 54.198 0.000
## .BSBS23F (.41.) 0.541 0.009 59.266 0.000
## .BSBS23G (.42.) 0.423 0.007 57.133 0.000
## .BSBS23H (.43.) 0.446 0.008 56.657 0.000
## .BSBS24A (.44.) 0.311 0.006 56.452 0.000
## .BSBS24B (.45.) 0.428 0.007 57.697 0.000
## .BSBS24C (.46.) 0.254 0.005 52.869 0.000
## .BSBS24D (.47.) 0.331 0.006 53.293 0.000
## .BSBS24E (.48.) 0.507 0.009 56.693 0.000
## .BSBS24F (.49.) 0.301 0.005 55.277 0.000
## .BSBS24G (.50.) 0.251 0.005 53.971 0.000
## .BSBS24H (.51.) 0.341 0.006 59.065 0.000
## .BSBS24I (.52.) 0.227 0.004 56.771 0.000
## lk_lrnn (.53.) 0.616 0.013 49.227 0.000
## confdnt (.54.) 0.341 0.009 39.408 0.000
## value (.55.) 0.408 0.011 38.345 0.000
##
##
## Group 2 [Boy]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## like_learning =~
## BSBS21A 1.000
## BSBS21B (.p2.) -0.782 0.013 -60.527 0.000
## BSBS21C (.p3.) -0.875 0.011 -76.351 0.000
## BSBS21D (.p4.) 0.785 0.009 83.866 0.000
## BSBS21E (.p5.) 1.080 0.009 123.619 0.000
## BSBS21F (.p6.) 1.087 0.010 112.237 0.000
## BSBS21G (.p7.) 0.587 0.009 62.628 0.000
## BSBS21H (.p8.) 0.516 0.010 49.609 0.000
## BSBS21I (.p9.) 1.155 0.011 108.538 0.000
## confident =~
## BSBS23A 1.000
## BSBS23B (.11.) -1.063 0.017 -63.496 0.000
## BSBS23C (.12.) -1.289 0.018 -71.518 0.000
## BSBS23D (.13.) 1.167 0.015 75.405 0.000
## BSBS23E (.14.) 1.175 0.017 70.955 0.000
## BSBS23F (.15.) 0.936 0.018 53.397 0.000
## BSBS23G (.16.) -1.065 0.017 -63.056 0.000
## BSBS23H (.17.) -1.141 0.018 -64.646 0.000
## value =~
## BSBS24A 1.000
## BSBS24B (.19.) 1.045 0.016 64.564 0.000
## BSBS24C (.20.) 1.138 0.015 75.728 0.000
## BSBS24D (.21.) 1.270 0.017 75.088 0.000
## BSBS24E (.22.) 1.250 0.018 67.845 0.000
## BSBS24F (.23.) 1.073 0.015 71.420 0.000
## BSBS24G (.24.) 1.065 0.014 73.970 0.000
## BSBS24H (.25.) 0.789 0.013 58.499 0.000
## BSBS24I (.26.) 0.831 0.012 67.616 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## like_learning ~~
## confdnt (.56.) 0.341 0.008 44.211 0.000
## value (.57.) 0.306 0.008 39.320 0.000
## confident ~~
## value (.58.) 0.190 0.006 33.491 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A (.59.) 1.970 0.013 146.474 0.000
## .BSBS21B (.60.) 2.719 0.013 202.055 0.000
## .BSBS21C (.61.) 2.829 0.013 210.477 0.000
## .BSBS21D (.62.) 1.741 0.012 150.054 0.000
## .BSBS21E (.63.) 1.997 0.014 140.746 0.000
## .BSBS21F (.64.) 2.203 0.015 150.519 0.000
## .BSBS21G (.65.) 1.641 0.010 165.499 0.000
## .BSBS21H (.66.) 1.575 0.010 157.526 0.000
## .BSBS21I (.67.) 2.337 0.016 148.944 0.000
## .BSBS23A (.68.) 1.879 0.011 171.607 0.000
## .BSBS23B (.69.) 2.923 0.012 235.026 0.000
## .BSBS23C (.70.) 2.663 0.014 188.632 0.000
## .BSBS23D (.71.) 2.124 0.012 170.772 0.000
## .BSBS23E (.72.) 2.358 0.013 182.468 0.000
## .BSBS23F (.73.) 2.417 0.012 198.186 0.000
## .BSBS23G (.74.) 2.999 0.013 239.790 0.000
## .BSBS23H (.75.) 2.801 0.013 212.009 0.000
## .BSBS24A (.76.) 1.859 0.012 153.874 0.000
## .BSBS24B (.77.) 2.127 0.013 162.877 0.000
## .BSBS24C (.78.) 1.783 0.013 136.802 0.000
## .BSBS24D (.79.) 1.987 0.015 136.021 0.000
## .BSBS24E (.80.) 2.303 0.015 151.608 0.000
## .BSBS24F (.81.) 1.855 0.013 146.382 0.000
## .BSBS24G (.82.) 1.713 0.012 138.829 0.000
## .BSBS24H (.83.) 1.640 0.010 156.515 0.000
## .BSBS24I (.84.) 1.539 0.010 152.111 0.000
## lk_lrnn -0.117 0.018 -6.415 0.000
## confdnt -0.122 0.014 -8.719 0.000
## value -0.001 0.015 -0.075 0.940
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .BSBS21A (.27.) 0.177 0.003 51.733 0.000
## .BSBS21B (.28.) 0.657 0.011 60.742 0.000
## .BSBS21C (.29.) 0.464 0.008 59.385 0.000
## .BSBS21D (.30.) 0.290 0.005 58.485 0.000
## .BSBS21E (.31.) 0.134 0.003 45.815 0.000
## .BSBS21F (.32.) 0.213 0.004 51.913 0.000
## .BSBS21G (.33.) 0.341 0.006 60.595 0.000
## .BSBS21H (.34.) 0.449 0.007 61.379 0.000
## .BSBS21I (.35.) 0.275 0.005 53.248 0.000
## .BSBS23A (.36.) 0.233 0.004 53.907 0.000
## .BSBS23B (.37.) 0.412 0.007 57.006 0.000
## .BSBS23C (.38.) 0.388 0.007 53.921 0.000
## .BSBS23D (.39.) 0.252 0.005 51.621 0.000
## .BSBS23E (.40.) 0.334 0.006 54.198 0.000
## .BSBS23F (.41.) 0.541 0.009 59.266 0.000
## .BSBS23G (.42.) 0.423 0.007 57.133 0.000
## .BSBS23H (.43.) 0.446 0.008 56.657 0.000
## .BSBS24A (.44.) 0.311 0.006 56.452 0.000
## .BSBS24B (.45.) 0.428 0.007 57.697 0.000
## .BSBS24C (.46.) 0.254 0.005 52.869 0.000
## .BSBS24D (.47.) 0.331 0.006 53.293 0.000
## .BSBS24E (.48.) 0.507 0.009 56.693 0.000
## .BSBS24F (.49.) 0.301 0.005 55.277 0.000
## .BSBS24G (.50.) 0.251 0.005 53.971 0.000
## .BSBS24H (.51.) 0.341 0.006 59.065 0.000
## .BSBS24I (.52.) 0.227 0.004 56.771 0.000
## lk_lrnn (.53.) 0.616 0.013 49.227 0.000
## confdnt (.54.) 0.341 0.009 39.408 0.000
## value (.55.) 0.408 0.011 38.345 0.000anova(science_cfa_4, science_cfa_5)#library(semTools)
#measurementInvariance(model = model_cfa, data=dat1, group="BSBG01")