Solution Lecture 8
Dr. Thomas Pollet, Northumbria University (thomas.pollet@northumbria.ac.uk)
2024-04-18 | disclaimer
Exercise 8 instructions.
Using the ‘bfi’ data from the ‘psych’ package, build a five factor model using lavaan.
Discuss the CFI, RMSEA and TLI of that model. Export a table with the factor loadings.
Make a plot.
Compare the fit of a five factor model to a single factor model (“The general factor of personality”).
Test the measurement invariance for men vs. women in the five factor model. Make a plot.
Make a table and discuss.
Load the data, set the working directory.
Load the data and get some descriptives.
## Loading required package: psych## Loading required package: skimr| Name | Data |
| Number of rows | 2800 |
| Number of columns | 28 |
| _______________________ | |
| Column type frequency: | |
| numeric | 28 |
| ________________________ | |
| Group variables | None |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| A1 | 16 | 0.99 | 2.41 | 1.41 | 1 | 1 | 2 | 3 | 6 | ▇▂▂▁▁ |
| A2 | 27 | 0.99 | 4.80 | 1.17 | 1 | 4 | 5 | 6 | 6 | ▂▁▅▇▇ |
| A3 | 26 | 0.99 | 4.60 | 1.30 | 1 | 4 | 5 | 6 | 6 | ▂▂▅▇▆ |
| A4 | 19 | 0.99 | 4.70 | 1.48 | 1 | 4 | 5 | 6 | 6 | ▂▁▃▅▇ |
| A5 | 16 | 0.99 | 4.56 | 1.26 | 1 | 4 | 5 | 5 | 6 | ▂▂▅▇▆ |
| C1 | 21 | 0.99 | 4.50 | 1.24 | 1 | 4 | 5 | 5 | 6 | ▂▂▅▇▅ |
| C2 | 24 | 0.99 | 4.37 | 1.32 | 1 | 4 | 5 | 5 | 6 | ▃▂▆▇▅ |
| C3 | 20 | 0.99 | 4.30 | 1.29 | 1 | 4 | 5 | 5 | 6 | ▃▂▆▇▅ |
| C4 | 26 | 0.99 | 2.55 | 1.38 | 1 | 1 | 2 | 4 | 6 | ▇▂▂▁▁ |
| C5 | 16 | 0.99 | 3.30 | 1.63 | 1 | 2 | 3 | 5 | 6 | ▇▂▅▃▂ |
| E1 | 23 | 0.99 | 2.97 | 1.63 | 1 | 2 | 3 | 4 | 6 | ▇▂▃▂▂ |
| E2 | 16 | 0.99 | 3.14 | 1.61 | 1 | 2 | 3 | 4 | 6 | ▇▂▃▂▂ |
| E3 | 25 | 0.99 | 4.00 | 1.35 | 1 | 3 | 4 | 5 | 6 | ▅▃▇▇▃ |
| E4 | 9 | 1.00 | 4.42 | 1.46 | 1 | 4 | 5 | 6 | 6 | ▃▂▃▇▆ |
| E5 | 21 | 0.99 | 4.42 | 1.33 | 1 | 4 | 5 | 5 | 6 | ▃▂▅▇▅ |
| N1 | 22 | 0.99 | 2.93 | 1.57 | 1 | 2 | 3 | 4 | 6 | ▇▂▃▂▁ |
| N2 | 21 | 0.99 | 3.51 | 1.53 | 1 | 2 | 4 | 5 | 6 | ▇▃▆▅▃ |
| N3 | 11 | 1.00 | 3.22 | 1.60 | 1 | 2 | 3 | 4 | 6 | ▇▂▅▃▂ |
| N4 | 36 | 0.99 | 3.19 | 1.57 | 1 | 2 | 3 | 4 | 6 | ▇▃▅▃▂ |
| N5 | 29 | 0.99 | 2.97 | 1.62 | 1 | 2 | 3 | 4 | 6 | ▇▂▃▂▂ |
| O1 | 22 | 0.99 | 4.82 | 1.13 | 1 | 4 | 5 | 6 | 6 | ▁▂▅▇▇ |
| O2 | 0 | 1.00 | 2.71 | 1.57 | 1 | 1 | 2 | 4 | 6 | ▇▂▂▂▁ |
| O3 | 28 | 0.99 | 4.44 | 1.22 | 1 | 4 | 5 | 5 | 6 | ▂▂▆▇▅ |
| O4 | 14 | 1.00 | 4.89 | 1.22 | 1 | 4 | 5 | 6 | 6 | ▁▁▃▆▇ |
| O5 | 20 | 0.99 | 2.49 | 1.33 | 1 | 1 | 2 | 3 | 6 | ▇▂▂▁▁ |
| gender | 0 | 1.00 | 1.67 | 0.47 | 1 | 1 | 2 | 2 | 2 | ▃▁▁▁▇ |
| education | 223 | 0.92 | 3.19 | 1.11 | 1 | 3 | 3 | 4 | 5 | ▂▂▇▂▃ |
| age | 0 | 1.00 | 28.78 | 11.13 | 3 | 20 | 26 | 35 | 86 | ▃▇▂▁▁ |
Subset data.
In exercise 7, we already examined the factorability, which was middling to meritorious. Therefore, we will proceed. Yet, it is worthwhile still exploring the assumption of multivariate normality.
Multivariate normality
There are some missings. You’ll get an error. Here I have listwise removed them.
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.054319 0 NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling A1 129.3201 <0.001 NO
## 2 Anderson-Darling A2 134.3857 <0.001 NO
## 3 Anderson-Darling A3 124.0838 <0.001 NO
## 4 Anderson-Darling A4 163.7947 <0.001 NO
## 5 Anderson-Darling A5 108.0415 <0.001 NO
## 6 Anderson-Darling C1 107.6637 <0.001 NO
## 7 Anderson-Darling C2 99.2526 <0.001 NO
## 8 Anderson-Darling C3 92.4993 <0.001 NO
## 9 Anderson-Darling C4 100.8417 <0.001 NO
## 10 Anderson-Darling C5 73.8674 <0.001 NO
## 11 Anderson-Darling E1 85.6666 <0.001 NO
## 12 Anderson-Darling E2 76.1363 <0.001 NO
## 13 Anderson-Darling E3 73.1035 <0.001 NO
## 14 Anderson-Darling E4 120.9196 <0.001 NO
## 15 Anderson-Darling E5 102.2867 <0.001 NO
## 16 Anderson-Darling N1 80.4836 <0.001 NO
## 17 Anderson-Darling N2 62.6557 <0.001 NO
## 18 Anderson-Darling N3 73.6727 <0.001 NO
## 19 Anderson-Darling N4 67.8013 <0.001 NO
## 20 Anderson-Darling N5 85.0121 <0.001 NO
## 21 Anderson-Darling O1 122.7557 <0.001 NO
## 22 Anderson-Darling O2 106.5534 <0.001 NO
## 23 Anderson-Darling O3 95.7682 <0.001 NO
## 24 Anderson-Darling O4 159.2082 <0.001 NO
## 25 Anderson-Darling O5 105.3923 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew Kurtosis
## A1 2436 2.406404 1.407177 2 1 6 1 3 0.83796401 -0.27990169
## A2 2436 4.797209 1.179535 5 1 6 4 6 -1.11880031 1.00641205
## A3 2436 4.598522 1.311355 5 1 6 4 6 -1.01376321 0.46427989
## A4 2436 4.687603 1.485213 5 1 6 4 6 -1.02356587 0.01565904
## A5 2436 4.543514 1.270804 5 1 6 4 5 -0.84391857 0.12691880
## C1 2436 4.525041 1.235258 5 1 6 4 5 -0.86637245 0.32227825
## C2 2436 4.372332 1.319152 5 1 6 4 5 -0.73780864 -0.15203946
## C3 2436 4.300082 1.291202 5 1 6 4 5 -0.67763595 -0.14737260
## C4 2436 2.549672 1.376689 2 1 6 1 4 0.61488991 -0.58893943
## C5 2436 3.305829 1.632720 3 1 6 2 5 0.06052881 -1.23223720
## E1 2436 2.978654 1.631428 3 1 6 2 4 0.37410317 -1.09332917
## E2 2436 3.154351 1.613847 3 1 6 2 4 0.22661706 -1.15162025
## E3 2436 3.984401 1.351766 4 1 6 3 5 -0.46630447 -0.45987134
## E4 2436 4.408867 1.467060 5 1 6 4 6 -0.82073539 -0.31981004
## E5 2436 4.390805 1.343316 5 1 6 4 5 -0.77849487 -0.11090601
## N1 2436 2.943760 1.575909 3 1 6 2 4 0.36897054 -1.02086962
## N2 2436 3.517652 1.533238 4 1 6 2 5 -0.08250293 -1.05865697
## N3 2436 3.224548 1.594674 3 1 6 2 5 0.14112304 -1.18071647
## N4 2436 3.202381 1.569633 3 1 6 2 4 0.19727510 -1.08501749
## N5 2436 2.971264 1.623491 3 1 6 2 4 0.37734052 -1.06769970
## O1 2436 4.812808 1.126613 5 1 6 4 6 -0.90440484 0.45739679
## O2 2436 2.684729 1.552883 2 1 6 1 4 0.61587159 -0.76351993
## O3 2436 4.449918 1.205206 5 1 6 4 5 -0.76957250 0.32182294
## O4 2436 4.925287 1.193136 5 1 6 4 6 -1.23792688 1.17547750
## O5 2436 2.468801 1.324021 2 1 6 1 3 0.76398033 -0.18446774We should bear in mind that the assumption of multivariate normality is violated.
Lavaan model.
## Loading required package: lavaan## This is lavaan 0.6-17
## lavaan is FREE software! Please report any bugs.##
## Attaching package: 'lavaan'## The following object is masked from 'package:psych':
##
## cor2covfive_factor <- ' # Five factors.
Agreeable =~ A1 + A2 + A3 + A4 + A5
Conscientous =~ C1 + C2 + C3 + C4 + C5
Extraversion =~ E1 + E2 + E3 + E4 + E5
Neurotic =~ N1 + N2 + N3 + N4 + N5
Opennness =~ O1 + O2 + O3 + O4 + O5'
fit_CFA<-cfa(five_factor, data= Data)Let us examine that massive output file… . As you can see the model converged after 55 iterations. 2436 from the 2800 observations were used (listwise deletion). Read here for other settings.
While the five factor model could be considered an acceptable fit in RMSEA (.078), it was not in terms of TLI (.754) and CFI (.782). (check here)
## lavaan 0.6.17 ended normally after 55 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 60
##
## Used Total
## Number of observations 2436 2800
##
## Model Test User Model:
##
## Test statistic 4165.467
## Degrees of freedom 265
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 18222.116
## Degrees of freedom 300
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.782
## Tucker-Lewis Index (TLI) 0.754
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -99840.238
## Loglikelihood unrestricted model (H1) -97757.504
##
## Akaike (AIC) 199800.476
## Bayesian (BIC) 200148.363
## Sample-size adjusted Bayesian (SABIC) 199957.729
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.078
## 90 Percent confidence interval - lower 0.076
## 90 Percent confidence interval - upper 0.080
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.037
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.075
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## Agreeable =~
## A1 1.000
## A2 -1.579 0.108 -14.650 0.000
## A3 -2.030 0.134 -15.093 0.000
## A4 -1.564 0.115 -13.616 0.000
## A5 -1.804 0.121 -14.852 0.000
## Conscientous =~
## C1 1.000
## C2 1.148 0.057 20.152 0.000
## C3 1.036 0.054 19.172 0.000
## C4 -1.421 0.065 -21.924 0.000
## C5 -1.489 0.072 -20.694 0.000
## Extraversion =~
## E1 1.000
## E2 1.226 0.051 23.899 0.000
## E3 -0.921 0.041 -22.431 0.000
## E4 -1.121 0.047 -23.977 0.000
## E5 -0.808 0.039 -20.648 0.000
## Neurotic =~
## N1 1.000
## N2 0.947 0.024 39.899 0.000
## N3 0.884 0.025 35.919 0.000
## N4 0.692 0.025 27.753 0.000
## N5 0.628 0.026 24.027 0.000
## Opennness =~
## O1 1.000
## O2 -1.020 0.068 -14.962 0.000
## O3 1.373 0.072 18.942 0.000
## O4 0.437 0.048 9.160 0.000
## O5 -0.960 0.060 -16.056 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## Agreeable ~~
## Conscientous -0.110 0.012 -9.254 0.000
## Extraversion 0.304 0.025 12.293 0.000
## Neurotic 0.141 0.018 7.712 0.000
## Opennness -0.093 0.011 -8.446 0.000
## Conscientous ~~
## Extraversion -0.224 0.020 -11.121 0.000
## Neurotic -0.250 0.025 -10.117 0.000
## Opennness 0.130 0.014 9.190 0.000
## Extraversion ~~
## Neurotic 0.292 0.032 9.131 0.000
## Opennness -0.265 0.021 -12.347 0.000
## Neurotic ~~
## Opennness -0.093 0.022 -4.138 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .A1 1.745 0.052 33.725 0.000
## .A2 0.807 0.028 28.396 0.000
## .A3 0.754 0.032 23.339 0.000
## .A4 1.632 0.051 31.796 0.000
## .A5 0.852 0.032 26.800 0.000
## .C1 1.063 0.035 30.073 0.000
## .C2 1.130 0.039 28.890 0.000
## .C3 1.170 0.039 30.194 0.000
## .C4 0.960 0.040 24.016 0.000
## .C5 1.640 0.059 27.907 0.000
## .E1 1.814 0.058 31.047 0.000
## .E2 1.332 0.049 26.928 0.000
## .E3 1.108 0.038 29.522 0.000
## .E4 1.088 0.041 26.732 0.000
## .E5 1.251 0.040 31.258 0.000
## .N1 0.793 0.037 21.575 0.000
## .N2 0.836 0.036 23.458 0.000
## .N3 1.222 0.043 28.271 0.000
## .N4 1.654 0.052 31.977 0.000
## .N5 1.969 0.060 32.889 0.000
## .O1 0.865 0.032 27.216 0.000
## .O2 1.990 0.063 31.618 0.000
## .O3 0.691 0.039 17.717 0.000
## .O4 1.346 0.040 34.036 0.000
## .O5 1.380 0.045 30.662 0.000
## Agreeable 0.234 0.030 7.839 0.000
## Conscientous 0.463 0.036 12.810 0.000
## Extraversion 0.846 0.062 13.693 0.000
## Neurotic 1.689 0.073 23.034 0.000
## Opennness 0.404 0.033 12.156 0.000Remember that multivariate normality issue?
Lavaan offers many options… .
The conclusions are by and large the same. Note that the standard errors are now robust. Can you spot the similarities and differences between the ‘original’ and the model with robust errors?
## lavaan 0.6.17 ended normally after 55 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 60
##
## Used Total
## Number of observations 2436 2800
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 4165.467 3612.178
## Degrees of freedom 265 265
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.153
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 18222.116 15289.285
## Degrees of freedom 300 300
## P-value 0.000 0.000
## Scaling correction factor 1.192
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.782 0.777
## Tucker-Lewis Index (TLI) 0.754 0.747
##
## Robust Comparative Fit Index (CFI) 0.784
## Robust Tucker-Lewis Index (TLI) 0.755
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -99840.238 -99840.238
## Scaling correction factor 1.216
## for the MLR correction
## Loglikelihood unrestricted model (H1) -97757.504 -97757.504
## Scaling correction factor 1.165
## for the MLR correction
##
## Akaike (AIC) 199800.476 199800.476
## Bayesian (BIC) 200148.363 200148.363
## Sample-size adjusted Bayesian (SABIC) 199957.729 199957.729
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.078 0.072
## 90 Percent confidence interval - lower 0.076 0.070
## 90 Percent confidence interval - upper 0.080 0.074
## P-value H_0: RMSEA <= 0.050 0.000 0.000
## P-value H_0: RMSEA >= 0.080 0.037 0.000
##
## Robust RMSEA 0.077
## 90 Percent confidence interval - lower 0.075
## 90 Percent confidence interval - upper 0.080
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 0.025
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.075 0.075
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## Agreeable =~
## A1 1.000
## A2 -1.579 0.110 -14.344 0.000
## A3 -2.030 0.148 -13.750 0.000
## A4 -1.564 0.128 -12.201 0.000
## A5 -1.804 0.145 -12.407 0.000
## Conscientous =~
## C1 1.000
## C2 1.148 0.051 22.376 0.000
## C3 1.036 0.061 17.032 0.000
## C4 -1.421 0.090 -15.828 0.000
## C5 -1.489 0.103 -14.402 0.000
## Extraversion =~
## E1 1.000
## E2 1.226 0.044 27.641 0.000
## E3 -0.921 0.049 -18.870 0.000
## E4 -1.121 0.046 -24.109 0.000
## E5 -0.808 0.045 -17.840 0.000
## Neurotic =~
## N1 1.000
## N2 0.947 0.017 55.953 0.000
## N3 0.884 0.029 30.726 0.000
## N4 0.692 0.033 20.713 0.000
## N5 0.628 0.032 19.878 0.000
## Opennness =~
## O1 1.000
## O2 -1.020 0.084 -12.094 0.000
## O3 1.373 0.087 15.803 0.000
## O4 0.437 0.054 8.153 0.000
## O5 -0.960 0.075 -12.854 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## Agreeable ~~
## Conscientous -0.110 0.013 -8.670 0.000
## Extraversion 0.304 0.025 12.231 0.000
## Neurotic 0.141 0.021 6.776 0.000
## Opennness -0.093 0.012 -7.832 0.000
## Conscientous ~~
## Extraversion -0.224 0.021 -10.413 0.000
## Neurotic -0.250 0.026 -9.670 0.000
## Opennness 0.130 0.018 7.080 0.000
## Extraversion ~~
## Neurotic 0.292 0.034 8.538 0.000
## Opennness -0.265 0.025 -10.512 0.000
## Neurotic ~~
## Opennness -0.093 0.026 -3.588 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .A1 1.745 0.058 29.920 0.000
## .A2 0.807 0.042 19.134 0.000
## .A3 0.754 0.046 16.464 0.000
## .A4 1.632 0.060 27.148 0.000
## .A5 0.852 0.046 18.657 0.000
## .C1 1.063 0.053 20.092 0.000
## .C2 1.130 0.052 21.820 0.000
## .C3 1.170 0.044 26.585 0.000
## .C4 0.960 0.054 17.824 0.000
## .C5 1.640 0.069 23.873 0.000
## .E1 1.814 0.061 29.746 0.000
## .E2 1.332 0.062 21.647 0.000
## .E3 1.108 0.046 23.844 0.000
## .E4 1.088 0.051 21.169 0.000
## .E5 1.251 0.047 26.587 0.000
## .N1 0.793 0.050 15.831 0.000
## .N2 0.836 0.049 17.060 0.000
## .N3 1.222 0.053 23.117 0.000
## .N4 1.654 0.060 27.546 0.000
## .N5 1.969 0.061 32.246 0.000
## .O1 0.865 0.038 22.625 0.000
## .O2 1.990 0.072 27.796 0.000
## .O3 0.691 0.053 13.126 0.000
## .O4 1.346 0.054 25.153 0.000
## .O5 1.380 0.060 22.984 0.000
## Agreeable 0.234 0.034 6.973 0.000
## Conscientous 0.463 0.046 10.015 0.000
## Extraversion 0.846 0.064 13.211 0.000
## Neurotic 1.689 0.069 24.518 0.000
## Opennness 0.404 0.036 11.073 0.000Residual check
Some issues with correlated residuals. This basically allow us to see where we ‘mess up’. You could attempt explicitly modelling those correlations?
require(ggplot2)
require(corrplot)
plot_matrix <- function(matrix_toplot){
corrplot(matrix_toplot, is.corr = FALSE,
type = 'lower',
order = "original",
tl.col='black', tl.cex=.75)}
plot_matrix(residuals(fit_CFA)$cov)
require(lavaan)
five_factor_cor <- ' # Five factors.
Agreeable =~ A1 + A2 + A3 + A4 + A5
Conscientous =~ C1 + C2 + C3 + C4 + C5
Extraversion =~ E1 + E2 + E3 + E4 + E5
Neurotic =~ N1 + N2 + N3 + N4 + N5
Opennness =~ O1 + O2 + O3 + O4 + O5
# Some residuals can covary.
N4 ~~ C5
N4 ~~ E2
N4 ~~ E4'
fit_CFA_cor<-cfa(five_factor_cor, data= Data)In this case, we have improved in terms of fit.
## lavaan 0.6.17 ended normally after 57 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 63
##
## Used Total
## Number of observations 2436 2800
##
## Model Test User Model:
##
## Test statistic 4008.238
## Degrees of freedom 262
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 18222.116
## Degrees of freedom 300
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.791
## Tucker-Lewis Index (TLI) 0.761
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -99761.623
## Loglikelihood unrestricted model (H1) -97757.504
##
## Akaike (AIC) 199649.247
## Bayesian (BIC) 200014.528
## Sample-size adjusted Bayesian (SABIC) 199814.362
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.077
## 90 Percent confidence interval - lower 0.075
## 90 Percent confidence interval - upper 0.079
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.004
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.074
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## Agreeable =~
## A1 1.000
## A2 -1.577 0.108 -14.667 0.000
## A3 -2.027 0.134 -15.111 0.000
## A4 -1.562 0.115 -13.626 0.000
## A5 -1.805 0.121 -14.874 0.000
## Conscientous =~
## C1 1.000
## C2 1.153 0.056 20.449 0.000
## C3 1.028 0.053 19.310 0.000
## C4 -1.386 0.063 -21.919 0.000
## C5 -1.385 0.068 -20.374 0.000
## Extraversion =~
## E1 1.000
## E2 1.194 0.052 23.054 0.000
## E3 -0.949 0.043 -22.191 0.000
## E4 -1.100 0.047 -23.206 0.000
## E5 -0.813 0.040 -20.179 0.000
## Neurotic =~
## N1 1.000
## N2 0.940 0.023 40.107 0.000
## N3 0.868 0.024 35.741 0.000
## N4 0.608 0.024 25.720 0.000
## N5 0.614 0.026 23.770 0.000
## Opennness =~
## O1 1.000
## O2 -1.018 0.068 -14.983 0.000
## O3 1.371 0.072 19.042 0.000
## O4 0.435 0.048 9.158 0.000
## O5 -0.956 0.059 -16.066 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .C5 ~~
## .N4 0.338 0.038 8.947 0.000
## .E2 ~~
## .N4 0.222 0.035 6.367 0.000
## .E4 ~~
## .N4 -0.190 0.031 -6.035 0.000
## Agreeable ~~
## Conscientous -0.110 0.012 -9.211 0.000
## Extraversion 0.302 0.025 12.266 0.000
## Neurotic 0.142 0.018 7.713 0.000
## Opennness -0.094 0.011 -8.457 0.000
## Conscientous ~~
## Extraversion -0.212 0.020 -10.679 0.000
## Neurotic -0.246 0.025 -9.788 0.000
## Opennness 0.133 0.014 9.263 0.000
## Extraversion ~~
## Neurotic 0.273 0.032 8.632 0.000
## Opennness -0.267 0.021 -12.452 0.000
## Neurotic ~~
## Opennness -0.099 0.023 -4.379 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .A1 1.745 0.052 33.728 0.000
## .A2 0.807 0.028 28.430 0.000
## .A3 0.755 0.032 23.419 0.000
## .A4 1.633 0.051 31.817 0.000
## .A5 0.850 0.032 26.803 0.000
## .C1 1.050 0.035 29.773 0.000
## .C2 1.108 0.039 28.399 0.000
## .C3 1.164 0.039 30.016 0.000
## .C4 0.982 0.040 24.280 0.000
## .C5 1.688 0.059 28.753 0.000
## .E1 1.844 0.059 31.146 0.000
## .E2 1.367 0.050 27.503 0.000
## .E3 1.090 0.037 29.139 0.000
## .E4 1.106 0.041 27.131 0.000
## .E5 1.263 0.040 31.276 0.000
## .N1 0.759 0.037 20.614 0.000
## .N2 0.826 0.036 23.100 0.000
## .N3 1.245 0.044 28.493 0.000
## .N4 1.683 0.051 32.691 0.000
## .N5 1.985 0.060 32.954 0.000
## .O1 0.864 0.032 27.238 0.000
## .O2 1.991 0.063 31.646 0.000
## .O3 0.691 0.039 17.804 0.000
## .O4 1.346 0.040 34.045 0.000
## .O5 1.382 0.045 30.717 0.000
## Agreeable 0.235 0.030 7.848 0.000
## Conscientous 0.475 0.037 12.960 0.000
## Extraversion 0.817 0.061 13.368 0.000
## Neurotic 1.723 0.074 23.302 0.000
## Opennness 0.405 0.033 12.200 0.000Table
Here I have include the table rather than exported. In order to export it, you would use ‘out=’ . You view the example in class.
require(dplyr)
require(stargazer)
results_table<-parameterEstimates(fit_CFA, standardized=TRUE) %>%
filter(op == "=~") %>%
dplyr::select('Latent Factor'=lhs, Indicator=rhs, B=est, SE=se, Z=z, 'p value'=pvalue, Beta=std.all)
#export via stargazer. (Other options are ??xtable)
stargazer(results_table, summary = FALSE, type='html', header = F)| Latent Factor | Indicator | B | SE | Z | p value | Beta | |
| 1 | Agreeable | A1 | 1 | 0 | 0.344 | ||
| 2 | Agreeable | A2 | -1.579 | 0.108 | -14.650 | 0 | -0.648 |
| 3 | Agreeable | A3 | -2.030 | 0.134 | -15.093 | 0 | -0.749 |
| 4 | Agreeable | A4 | -1.564 | 0.115 | -13.616 | 0 | -0.510 |
| 5 | Agreeable | A5 | -1.804 | 0.121 | -14.852 | 0 | -0.687 |
| 6 | Conscientous | C1 | 1 | 0 | 0.551 | ||
| 7 | Conscientous | C2 | 1.148 | 0.057 | 20.152 | 0 | 0.592 |
| 8 | Conscientous | C3 | 1.036 | 0.054 | 19.172 | 0 | 0.546 |
| 9 | Conscientous | C4 | -1.421 | 0.065 | -21.924 | 0 | -0.702 |
| 10 | Conscientous | C5 | -1.489 | 0.072 | -20.694 | 0 | -0.620 |
| 11 | Extraversion | E1 | 1 | 0 | 0.564 | ||
| 12 | Extraversion | E2 | 1.226 | 0.051 | 23.899 | 0 | 0.699 |
| 13 | Extraversion | E3 | -0.921 | 0.041 | -22.431 | 0 | -0.627 |
| 14 | Extraversion | E4 | -1.121 | 0.047 | -23.977 | 0 | -0.703 |
| 15 | Extraversion | E5 | -0.808 | 0.039 | -20.648 | 0 | -0.553 |
| 16 | Neurotic | N1 | 1 | 0 | 0.825 | ||
| 17 | Neurotic | N2 | 0.947 | 0.024 | 39.899 | 0 | 0.803 |
| 18 | Neurotic | N3 | 0.884 | 0.025 | 35.919 | 0 | 0.721 |
| 19 | Neurotic | N4 | 0.692 | 0.025 | 27.753 | 0 | 0.573 |
| 20 | Neurotic | N5 | 0.628 | 0.026 | 24.027 | 0 | 0.503 |
| 21 | Opennness | O1 | 1 | 0 | 0.564 | ||
| 22 | Opennness | O2 | -1.020 | 0.068 | -14.962 | 0 | -0.418 |
| 23 | Opennness | O3 | 1.373 | 0.072 | 18.942 | 0 | 0.724 |
| 24 | Opennness | O4 | 0.437 | 0.048 | 9.160 | 0 | 0.233 |
| 25 | Opennness | O5 | -0.960 | 0.060 | -16.056 | 0 | -0.461 |
O4 scores poor in terms of loadings (\(\beta\)<.3), A1 also does not load very well on its alledged factor (\(\beta\)<.4).
Figure.
One factor solution.
require(lavaan)
one_factor <- ' # One factor.
General =~ A1 + A2 + A3 + A4 + A5 + C1 + C2 + C3 + C4 + C5 + E1 + E2 + E3 + E4 + E5 + N1 + N2 + N3 + N4 + N5 + O1 + O2 + O3 + O4 + O5'
fit_CFA_one<-cfa(one_factor, data= Data)Fit measures. A quick glance at RMSEA, CFI and GFI already tells you that this is not looking great.
## lavaan 0.6.17 ended normally after 65 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 50
##
## Used Total
## Number of observations 2436 2800
##
## Model Test User Model:
##
## Test statistic 10673.239
## Degrees of freedom 275
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 18222.116
## Degrees of freedom 300
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.420
## Tucker-Lewis Index (TLI) 0.367
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -103094.124
## Loglikelihood unrestricted model (H1) -97757.504
##
## Akaike (AIC) 206288.248
## Bayesian (BIC) 206578.154
## Sample-size adjusted Bayesian (SABIC) 206419.292
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.125
## 90 Percent confidence interval - lower 0.123
## 90 Percent confidence interval - upper 0.127
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.116
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## General =~
## A1 1.000
## A2 -1.819 0.191 -9.520 0.000
## A3 -2.329 0.239 -9.750 0.000
## A4 -2.065 0.222 -9.319 0.000
## A5 -2.489 0.252 -9.882 0.000
## C1 -1.242 0.146 -8.495 0.000
## C2 -1.277 0.152 -8.377 0.000
## C3 -1.201 0.146 -8.250 0.000
## C4 1.778 0.194 9.158 0.000
## C5 2.346 0.250 9.386 0.000
## E1 2.346 0.250 9.387 0.000
## E2 3.291 0.331 9.930 0.000
## E3 -2.434 0.249 -9.770 0.000
## E4 -2.999 0.302 -9.933 0.000
## E5 -2.277 0.235 -9.679 0.000
## N1 1.762 0.200 8.797 0.000
## N2 1.689 0.193 8.757 0.000
## N3 1.690 0.195 8.649 0.000
## N4 2.423 0.254 9.522 0.000
## N5 1.557 0.187 8.349 0.000
## O1 -1.155 0.135 -8.552 0.000
## O2 0.782 0.132 5.919 0.000
## O3 -1.544 0.169 -9.140 0.000
## O4 0.250 0.087 2.859 0.004
## O5 0.733 0.116 6.302 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .A1 1.883 0.054 34.598 0.000
## .A2 1.072 0.032 33.143 0.000
## .A3 1.196 0.037 32.314 0.000
## .A4 1.794 0.053 33.548 0.000
## .A5 1.017 0.032 31.425 0.000
## .C1 1.376 0.040 34.262 0.000
## .C2 1.582 0.046 34.314 0.000
## .C3 1.528 0.044 34.363 0.000
## .C4 1.590 0.047 33.768 0.000
## .C5 2.134 0.064 33.432 0.000
## .E1 2.130 0.064 33.430 0.000
## .E2 1.560 0.050 30.939 0.000
## .E3 1.255 0.039 32.209 0.000
## .E4 1.284 0.042 30.906 0.000
## .E5 1.304 0.040 32.635 0.000
## .N1 2.183 0.064 34.091 0.000
## .N2 2.075 0.061 34.118 0.000
## .N3 2.267 0.066 34.183 0.000
## .N4 1.897 0.057 33.138 0.000
## .N5 2.401 0.070 34.325 0.000
## .O1 1.140 0.033 34.234 0.000
## .O2 2.351 0.068 34.752 0.000
## .O3 1.222 0.036 33.790 0.000
## .O4 1.417 0.041 34.875 0.000
## .O5 1.701 0.049 34.720 0.000
## General 0.096 0.019 5.104 0.000Group comparison model.
five_factor_groups <- ' # Five factors.
Agreeable =~ A1 + A2 + A3 + A4 + A5
Conscientous =~ C1 + C2 + C3 + C4 + C5
Extraversion =~ E1 + E2 + E3 + E4 + E5
Neurotic =~ N1 + N2 + N3 + N4 + N5
Opennness =~ O1 + O2 + O3 + O4 + O5'
fit_CFA_groups<-cfa(five_factor_groups, data= Data, group="gender")Massive output again. Notice how there are fewer men (1) than women (2).
## lavaan 0.6.17 ended normally after 100 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 170
##
## Number of observations per group: Used Total
## 1 805 919
## 2 1631 1881
##
## Model Test User Model:
##
## Test statistic 4545.267
## Degrees of freedom 530
## P-value (Chi-square) 0.000
## Test statistic for each group:
## 1 1673.974
## 2 2871.293
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## Agreeable =~
## A1 1.000
## A2 -1.806 0.232 -7.799 0.000
## A3 -2.267 0.282 -8.052 0.000
## A4 -1.708 0.232 -7.374 0.000
## A5 -2.181 0.272 -8.015 0.000
## Conscientous =~
## C1 1.000
## C2 1.125 0.098 11.471 0.000
## C3 1.003 0.094 10.722 0.000
## C4 -1.430 0.114 -12.574 0.000
## C5 -1.527 0.127 -12.042 0.000
## Extraversion =~
## E1 1.000
## E2 1.215 0.081 14.933 0.000
## E3 -0.919 0.067 -13.811 0.000
## E4 -1.152 0.077 -15.003 0.000
## E5 -0.879 0.065 -13.544 0.000
## Neurotic =~
## N1 1.000
## N2 0.966 0.046 20.952 0.000
## N3 0.862 0.045 18.964 0.000
## N4 0.745 0.047 15.830 0.000
## N5 0.552 0.045 12.320 0.000
## Opennness =~
## O1 1.000
## O2 -0.984 0.120 -8.196 0.000
## O3 1.356 0.128 10.621 0.000
## O4 0.518 0.088 5.892 0.000
## O5 -1.036 0.111 -9.315 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## Agreeable ~~
## Conscientous -0.089 0.019 -4.796 0.000
## Extraversion 0.295 0.044 6.762 0.000
## Neurotic 0.108 0.028 3.869 0.000
## Opennness -0.081 0.018 -4.636 0.000
## Conscientous ~~
## Extraversion -0.268 0.038 -7.061 0.000
## Neurotic -0.266 0.043 -6.215 0.000
## Opennness 0.135 0.025 5.485 0.000
## Extraversion ~~
## Neurotic 0.289 0.056 5.166 0.000
## Opennness -0.221 0.035 -6.306 0.000
## Neurotic ~~
## Opennness -0.054 0.037 -1.458 0.145
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .A1 2.722 0.050 54.042 0.000
## .A2 4.481 0.045 100.003 0.000
## .A3 4.334 0.047 92.228 0.000
## .A4 4.427 0.052 84.499 0.000
## .A5 4.361 0.047 93.244 0.000
## .C1 4.507 0.043 104.245 0.000
## .C2 4.255 0.047 91.057 0.000
## .C3 4.207 0.046 90.966 0.000
## .C4 2.687 0.050 54.023 0.000
## .C5 3.489 0.058 59.872 0.000
## .E1 3.267 0.059 55.599 0.000
## .E2 3.281 0.057 57.217 0.000
## .E3 3.902 0.049 79.443 0.000
## .E4 4.235 0.054 78.568 0.000
## .E5 4.256 0.048 88.011 0.000
## .N1 2.845 0.055 51.443 0.000
## .N2 3.288 0.054 60.772 0.000
## .N3 2.940 0.054 54.258 0.000
## .N4 3.201 0.056 57.403 0.000
## .N5 2.476 0.052 47.228 0.000
## .O1 4.990 0.038 131.870 0.000
## .O2 2.589 0.054 47.925 0.000
## .O3 4.522 0.043 105.746 0.000
## .O4 4.957 0.042 116.875 0.000
## .O5 2.394 0.048 50.395 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .A1 1.840 0.094 19.556 0.000
## .A2 0.957 0.057 16.807 0.000
## .A3 0.739 0.056 13.318 0.000
## .A4 1.621 0.088 18.368 0.000
## .A5 0.800 0.056 14.270 0.000
## .C1 1.039 0.061 17.165 0.000
## .C2 1.168 0.070 16.791 0.000
## .C3 1.254 0.071 17.656 0.000
## .C4 1.040 0.074 14.090 0.000
## .C5 1.648 0.105 15.764 0.000
## .E1 1.826 0.102 17.916 0.000
## .E2 1.238 0.081 15.329 0.000
## .E3 1.137 0.066 17.141 0.000
## .E4 1.073 0.071 15.156 0.000
## .E5 1.146 0.066 17.413 0.000
## .N1 0.900 0.069 12.987 0.000
## .N2 0.901 0.067 13.450 0.000
## .N3 1.205 0.074 16.209 0.000
## .N4 1.636 0.091 17.981 0.000
## .N5 1.737 0.091 19.000 0.000
## .O1 0.768 0.051 15.006 0.000
## .O2 1.976 0.108 18.262 0.000
## .O3 0.765 0.069 11.068 0.000
## .O4 1.344 0.070 19.341 0.000
## .O5 1.404 0.082 17.207 0.000
## Agreeable 0.202 0.049 4.133 0.000
## Conscientous 0.465 0.063 7.430 0.000
## Extraversion 0.953 0.114 8.357 0.000
## Neurotic 1.562 0.126 12.410 0.000
## Opennness 0.385 0.055 7.035 0.000
##
##
## Group 2 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## Agreeable =~
## A1 1.000
## A2 -1.531 0.136 -11.294 0.000
## A3 -2.074 0.178 -11.630 0.000
## A4 -1.577 0.151 -10.452 0.000
## A5 -1.799 0.158 -11.413 0.000
## Conscientous =~
## C1 1.000
## C2 1.143 0.070 16.408 0.000
## C3 1.045 0.066 15.790 0.000
## C4 -1.414 0.079 -17.912 0.000
## C5 -1.467 0.087 -16.805 0.000
## Extraversion =~
## E1 1.000
## E2 1.273 0.070 18.267 0.000
## E3 -0.960 0.055 -17.358 0.000
## E4 -1.127 0.062 -18.218 0.000
## E5 -0.786 0.051 -15.331 0.000
## Neurotic =~
## N1 1.000
## N2 0.927 0.027 33.767 0.000
## N3 0.885 0.029 30.411 0.000
## N4 0.682 0.029 23.169 0.000
## N5 0.635 0.031 20.360 0.000
## Opennness =~
## O1 1.000
## O2 -1.000 0.082 -12.241 0.000
## O3 1.404 0.088 15.993 0.000
## O4 0.401 0.057 7.084 0.000
## O5 -0.904 0.070 -12.936 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## Agreeable ~~
## Conscientous -0.104 0.014 -7.444 0.000
## Extraversion 0.265 0.028 9.565 0.000
## Neurotic 0.174 0.023 7.389 0.000
## Opennness -0.102 0.014 -7.384 0.000
## Conscientous ~~
## Extraversion -0.188 0.023 -8.330 0.000
## Neurotic -0.263 0.031 -8.584 0.000
## Opennness 0.132 0.017 7.617 0.000
## Extraversion ~~
## Neurotic 0.314 0.038 8.203 0.000
## Opennness -0.292 0.027 -10.813 0.000
## Neurotic ~~
## Opennness -0.096 0.028 -3.488 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .A1 2.251 0.034 66.380 0.000
## .A2 4.953 0.027 182.186 0.000
## .A3 4.729 0.032 149.206 0.000
## .A4 4.816 0.036 132.569 0.000
## .A5 4.633 0.031 151.909 0.000
## .C1 4.534 0.031 147.786 0.000
## .C2 4.430 0.032 136.416 0.000
## .C3 4.346 0.032 137.354 0.000
## .C4 2.482 0.034 74.039 0.000
## .C5 3.215 0.040 80.444 0.000
## .E1 2.836 0.039 71.867 0.000
## .E2 3.092 0.040 77.887 0.000
## .E3 4.025 0.033 122.375 0.000
## .E4 4.495 0.035 127.198 0.000
## .E5 4.457 0.033 136.018 0.000
## .N1 2.993 0.039 76.661 0.000
## .N2 3.631 0.038 96.528 0.000
## .N3 3.365 0.040 84.763 0.000
## .N4 3.203 0.039 82.766 0.000
## .N5 3.216 0.040 79.597 0.000
## .O1 4.725 0.028 167.191 0.000
## .O2 2.732 0.039 70.722 0.000
## .O3 4.414 0.030 148.657 0.000
## .O4 4.910 0.029 166.987 0.000
## .O5 2.506 0.032 77.241 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .A1 1.672 0.061 27.599 0.000
## .A2 0.729 0.031 23.276 0.000
## .A3 0.762 0.040 19.242 0.000
## .A4 1.646 0.063 26.115 0.000
## .A5 0.858 0.038 22.336 0.000
## .C1 1.076 0.044 24.693 0.000
## .C2 1.120 0.047 23.685 0.000
## .C3 1.131 0.046 24.538 0.000
## .C4 0.914 0.047 19.394 0.000
## .C5 1.616 0.070 22.975 0.000
## .E1 1.803 0.071 25.564 0.000
## .E2 1.375 0.062 22.122 0.000
## .E3 1.085 0.045 23.948 0.000
## .E4 1.100 0.049 22.249 0.000
## .E5 1.296 0.050 25.986 0.000
## .N1 0.746 0.043 17.277 0.000
## .N2 0.812 0.042 19.534 0.000
## .N3 1.209 0.052 23.196 0.000
## .N4 1.632 0.062 26.259 0.000
## .N5 1.960 0.073 26.908 0.000
## .O1 0.896 0.039 22.856 0.000
## .O2 2.027 0.077 26.193 0.000
## .O3 0.636 0.046 13.686 0.000
## .O4 1.344 0.048 28.001 0.000
## .O5 1.384 0.054 25.697 0.000
## Agreeable 0.204 0.034 6.065 0.000
## Conscientous 0.460 0.044 10.409 0.000
## Extraversion 0.737 0.070 10.519 0.000
## Neurotic 1.740 0.090 19.362 0.000
## Opennness 0.407 0.041 10.023 0.000
Measurement invariance table.
The best fitting model based on both AIC and BIC was one with metric invariance (respectively 199471 and 200341). In terms of RMSEA the model with metric invariance and that with strong invariance scored lowest and was thus the best fit (.077). In absolute terms, CFI favoured either the configural or the metric invariance model (0.775). While the metric invariance model is not an adequate fit in terms of CFI (0.775), it is in RMSEA (.077). Both the \(\Delta\)CFI and \(\Delta\)RMSEA suggested that there was no loss in fit moving from a configural model to a metric invariance model (all <.001).
##
## Measurement invariance models:
##
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
##
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit.configural 530 199494 200479 4545.3
## fit.loadings 550 199471 200341 4562.6 17.307 0.000000 20 0.6329
## fit.intercepts 570 199646 200400 4777.9 215.312 0.089542 20 <2e-16
## fit.means 575 199823 200547 4964.1 186.241 0.172512 5 <2e-16
##
## fit.configural
## fit.loadings
## fit.intercepts ***
## fit.means ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Fit measures:
##
## cfi rmsea cfi.delta rmsea.delta
## fit.configural 0.775 0.079 NA NA
## fit.loadings 0.775 0.077 0.000 0.001
## fit.intercepts 0.764 0.078 0.011 0.000
## fit.means 0.754 0.079 0.010 0.001Look at the beauty below… . If you want to export it. Check ‘xtable’.
require(psytabs)
require(knitr)
tab.1 <- measurementInvarianceTable(MI)
# kable!
colnames(tab.1) <- c("$\\chi^2$", "df", "$\\Delta\\chi^2$", "df", "p", "CFI", "$\\Delta$CFI", "RMSEA", "$\\Delta$RMSEA", "BIC", "$\\Delta$BIC")
kable(tab.1)| \(\chi^2\) | df | \(\Delta\chi^2\) | df | p | CFI | \(\Delta\)CFI | RMSEA | \(\Delta\)RMSEA | BIC | \(\Delta\)BIC | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Configural | 4545.3 | 530 | NA | NA | NA | 0.775 | NA | 0.079 | NA | 200479.4 | NA |
| Metric | 4562.6 | 550 | 17.3 | 20 | 0.633 | 0.775 | 0.000 | 0.077 | 0.001 | 200340.8 | 138.7 |
| Scalar | 4777.9 | 570 | 215.3 | 20 | 0.000 | 0.764 | 0.011 | 0.078 | 0.000 | 200400.1 | -59.3 |
| Mean | 4964.1 | 575 | 186.2 | 5 | 0.000 | 0.754 | 0.010 | 0.079 | -0.001 | 200547.4 | -147.3 |
THE END!
Session Info.
## R version 4.3.2 (2023-10-31)
## Platform: aarch64-apple-darwin20 (64-bit)
## Running under: macOS Ventura 13.4
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.11.0
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## time zone: Europe/London
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] knitr_1.45 psytabs_0.5-2 mokken_3.1.0
## [4] poLCA_1.6.0.1 MASS_7.3-60 scatterplot3d_0.3-44
## [7] R2HTML_2.2 rtf_0.4-14.1 plyr_1.8.9
## [10] semTools_0.5-6 qgraph_1.9.8 semPlot_1.1.6
## [13] stargazer_5.2.3 dplyr_1.1.3 corrplot_0.92
## [16] ggplot2_3.4.4 lavaan_0.6-17 MVN_5.9
## [19] skimr_2.1.5 psych_2.4.1
##
## loaded via a namespace (and not attached):
## [1] mnormt_2.1.1 pbapply_1.7-2 gridExtra_2.3
## [4] sandwich_3.0-2 fdrtool_1.2.17 rlang_1.1.3
## [7] magrittr_2.0.3 multcomp_1.4-25 rockchalk_1.8.157
## [10] compiler_4.3.2 png_0.1-8 vctrs_0.6.5
## [13] reshape2_1.4.4 gsl_2.1-8 OpenMx_2.21.8
## [16] quadprog_1.5-8 stringr_1.5.1 pkgconfig_2.0.3
## [19] fastmap_1.1.1 arm_1.13-1 backports_1.4.1
## [22] energy_1.7-11 pbivnorm_0.6.0 utf8_1.2.4
## [25] rmarkdown_2.26 nloptr_2.0.3 purrr_1.0.2
## [28] xfun_0.43 cachem_1.0.8 kutils_1.73
## [31] jsonlite_1.8.8 highr_0.10 jpeg_0.1-10
## [34] parallel_4.3.2 cluster_2.1.4 R6_2.5.1
## [37] bslib_0.7.0 stringi_1.8.3 car_3.1-2
## [40] boot_1.3-28.1 rpart_4.1.21 estimability_1.4.1
## [43] jquerylib_0.1.4 Rcpp_1.0.11 zoo_1.8-12
## [46] base64enc_0.1-3 Matrix_1.6-1.1 splines_4.3.2
## [49] nnet_7.3-19 igraph_2.0.3 tidyselect_1.2.0
## [52] rstudioapi_0.16.0 abind_1.4-5 yaml_2.3.8
## [55] codetools_0.2-19 lattice_0.21-9 tibble_3.2.1
## [58] withr_2.5.2 coda_0.19-4 evaluate_0.23
## [61] moments_0.14.1 foreign_0.8-85 survival_3.5-7
## [64] RcppParallel_5.1.7 zip_2.3.0 pillar_1.9.0
## [67] carData_3.0-5 checkmate_2.3.0 nortest_1.0-4
## [70] stats4_4.3.2 generics_0.1.3 munsell_0.5.1
## [73] scales_1.3.0 minqa_1.2.6 gtools_3.9.4
## [76] xtable_1.8-4 glue_1.7.0 mi_1.1
## [79] emmeans_1.8.9 Hmisc_5.1-1 tools_4.3.2
## [82] data.table_1.14.10 lme4_1.1-35 openxlsx_4.2.5.2
## [85] mvtnorm_1.2-3 XML_3.99-0.15 grid_4.3.2
## [88] sem_3.1-15 tidyr_1.3.0 colorspace_2.1-0
## [91] nlme_3.1-163 repr_1.1.6 htmlTable_2.4.2
## [94] Formula_1.2-5 cli_3.6.2 fansi_1.0.6
## [97] corpcor_1.6.10 glasso_1.11 gtable_0.3.4
## [100] R.methodsS3_1.8.2 sass_0.4.9 digest_0.6.35
## [103] TH.data_1.1-2 htmlwidgets_1.6.2 R.oo_1.25.0
## [106] htmltools_0.5.8.1 lifecycle_1.0.4 lisrelToR_0.1.5