El análisis factorial confirmatorio trata de establecer si el número de factores obtenidos se corresponden con los que cabría esperar a la luz de una teoría previa acerca de los datos. Se considera como una forma de modelo de ecuaciones estructurales.
Se utilizan los datos de Holzinger y Swineford (1939) consiste en puntuaciones de pruebas de capacidad mental de niños de séptimo y octavo grado de dos escuelas diferentes, tomados del paquete levaan.
Solamente se utilizan las variables.
x1: Visual perception
x2: Cubes
x3: Lozenges
x4: Paragraph comprehension
x5: Sentence completion
x6: Word meaning
x7: Speeded addition
x8: Speeded counting of dots
x9: Speeded discrimination straight and curved capitals
dato<-data.frame(x1,x2,x3,x4,x5,x6,x7,x8,x9)
head(dato)## x1 x2 x3 x4 x5 x6 x7 x8 x9
## 1 3.333333 7.75 0.375 2.333333 5.75 1.2857143 3.391304 5.75 6.361111
## 2 5.333333 5.25 2.125 1.666667 3.00 1.2857143 3.782609 6.25 7.916667
## 3 4.500000 5.25 1.875 1.000000 1.75 0.4285714 3.260870 3.90 4.416667
## 4 5.333333 7.75 3.000 2.666667 4.50 2.4285714 3.000000 5.30 4.861111
## 5 4.833333 4.75 0.875 2.666667 4.00 2.5714286 3.695652 6.30 5.916667
## 6 5.333333 5.00 2.250 1.000000 3.00 0.8571429 4.347826 6.65 7.500000El modelo se obtuvo mediante el análisis factorial.
modelo<-"visual=~ x1 + x2 + x3
textual=~ x4 + x5 + x6
speed =~ x7 + x8 + x9"
fit<-cfa(model= modelo,
data = dato)
summary(fit) ## lavaan 0.6.16 ended normally after 35 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 21
##
## Number of observations 301
##
## Model Test User Model:
##
## Test statistic 85.306
## Degrees of freedom 24
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## visual =~
## x1 1.000
## x2 0.554 0.100 5.554 0.000
## x3 0.729 0.109 6.685 0.000
## textual =~
## x4 1.000
## x5 1.113 0.065 17.014 0.000
## x6 0.926 0.055 16.703 0.000
## speed =~
## x7 1.000
## x8 1.180 0.165 7.152 0.000
## x9 1.082 0.151 7.155 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## visual ~~
## textual 0.408 0.074 5.552 0.000
## speed 0.262 0.056 4.660 0.000
## textual ~~
## speed 0.173 0.049 3.518 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .x1 0.549 0.114 4.833 0.000
## .x2 1.134 0.102 11.146 0.000
## .x3 0.844 0.091 9.317 0.000
## .x4 0.371 0.048 7.779 0.000
## .x5 0.446 0.058 7.642 0.000
## .x6 0.356 0.043 8.277 0.000
## .x7 0.799 0.081 9.823 0.000
## .x8 0.488 0.074 6.573 0.000
## .x9 0.566 0.071 8.003 0.000
## visual 0.809 0.145 5.564 0.000
## textual 0.979 0.112 8.737 0.000
## speed 0.384 0.086 4.451 0.000summary(fit, fit.measures = TRUE, standardized = TRUE)## lavaan 0.6.16 ended normally after 35 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 21
##
## Number of observations 301
##
## Model Test User Model:
##
## Test statistic 85.306
## Degrees of freedom 24
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 918.852
## Degrees of freedom 36
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.931
## Tucker-Lewis Index (TLI) 0.896
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3737.745
## Loglikelihood unrestricted model (H1) -3695.092
##
## Akaike (AIC) 7517.490
## Bayesian (BIC) 7595.339
## Sample-size adjusted Bayesian (SABIC) 7528.739
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.092
## 90 Percent confidence interval - lower 0.071
## 90 Percent confidence interval - upper 0.114
## P-value H_0: RMSEA <= 0.050 0.001
## P-value H_0: RMSEA >= 0.080 0.840
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.065
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## visual =~
## x1 1.000 0.900 0.772
## x2 0.554 0.100 5.554 0.000 0.498 0.424
## x3 0.729 0.109 6.685 0.000 0.656 0.581
## textual =~
## x4 1.000 0.990 0.852
## x5 1.113 0.065 17.014 0.000 1.102 0.855
## x6 0.926 0.055 16.703 0.000 0.917 0.838
## speed =~
## x7 1.000 0.619 0.570
## x8 1.180 0.165 7.152 0.000 0.731 0.723
## x9 1.082 0.151 7.155 0.000 0.670 0.665
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## visual ~~
## textual 0.408 0.074 5.552 0.000 0.459 0.459
## speed 0.262 0.056 4.660 0.000 0.471 0.471
## textual ~~
## speed 0.173 0.049 3.518 0.000 0.283 0.283
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .x1 0.549 0.114 4.833 0.000 0.549 0.404
## .x2 1.134 0.102 11.146 0.000 1.134 0.821
## .x3 0.844 0.091 9.317 0.000 0.844 0.662
## .x4 0.371 0.048 7.779 0.000 0.371 0.275
## .x5 0.446 0.058 7.642 0.000 0.446 0.269
## .x6 0.356 0.043 8.277 0.000 0.356 0.298
## .x7 0.799 0.081 9.823 0.000 0.799 0.676
## .x8 0.488 0.074 6.573 0.000 0.488 0.477
## .x9 0.566 0.071 8.003 0.000 0.566 0.558
## visual 0.809 0.145 5.564 0.000 1.000 1.000
## textual 0.979 0.112 8.737 0.000 1.000 1.000
## speed 0.384 0.086 4.451 0.000 1.000 1.000modindices(fit, sort = TRUE, maximum.number = 10)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 30 visual =~ x9 36.411 0.577 0.519 0.515 0.515
## 76 x7 ~~ x8 34.145 0.536 0.536 0.859 0.859
## 28 visual =~ x7 18.631 -0.422 -0.380 -0.349 -0.349
## 78 x8 ~~ x9 14.946 -0.423 -0.423 -0.805 -0.805
## 33 textual =~ x3 9.151 -0.272 -0.269 -0.238 -0.238
## 55 x2 ~~ x7 8.918 -0.183 -0.183 -0.192 -0.192
## 31 textual =~ x1 8.903 0.350 0.347 0.297 0.297
## 51 x2 ~~ x3 8.532 0.218 0.218 0.223 0.223
## 59 x3 ~~ x5 7.858 -0.130 -0.130 -0.212 -0.212
## 26 visual =~ x5 7.441 -0.210 -0.189 -0.147 -0.147inspect(fit, what = "std")## $lambda
## visual textul speed
## x1 0.772 0.000 0.000
## x2 0.424 0.000 0.000
## x3 0.581 0.000 0.000
## x4 0.000 0.852 0.000
## x5 0.000 0.855 0.000
## x6 0.000 0.838 0.000
## x7 0.000 0.000 0.570
## x8 0.000 0.000 0.723
## x9 0.000 0.000 0.665
##
## $theta
## x1 x2 x3 x4 x5 x6 x7 x8 x9
## x1 0.404
## x2 0.000 0.821
## x3 0.000 0.000 0.662
## x4 0.000 0.000 0.000 0.275
## x5 0.000 0.000 0.000 0.000 0.269
## x6 0.000 0.000 0.000 0.000 0.000 0.298
## x7 0.000 0.000 0.000 0.000 0.000 0.000 0.676
## x8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.477
## x9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.558
##
## $psi
## visual textul speed
## visual 1.000
## textual 0.459 1.000
## speed 0.471 0.283 1.000-|—|—|
O.M.F.
-|—|—|
paquetes utilizados:
polycor, ggcorrplot
GPArotation, lavaan
tidyverse,semTools
semPlot,psych
MVN
diagram
lavaanPlot
piecewiseSEM
corrr
corrplot