Ecuaciones estructurales.
Orlando Moscote Flórez
2023-08-30
Más aplicaciones estadísticas en:
Definición.
El análisis de ecuaciones estructurales es una técnica multivariada utilizada en la evaluación de modelos que presentan relaciones entre variables. También es la técnica a utilizar cuando los modelos incluyen variables latentes, medidas a partir de dos o más variables observables.Un caso particular especialmente relevante de ecuaciones estructurales es el análisis factorial confirmatorio, utilizado para evaluar la validez de constructo de escalas de medida.
Los modelos de ecuaciones estructurales permiten evaluar si un modelo que expresa una determinada relación entre las variables observables se ajusta a los datos muestrales. La evaluación de un modelo requiere una primera fase de especificación de tal modelo, seguida de las fases de identificación y de estimación. En la fase de especificación se definen las relaciones a evaluar entre variables. .
Datos utilizados.
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 de ecuaciones estructurales.
modelo5 <-" visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9 "modelo6<-sem(model= modelo5,
data= dato)summary(modelo6, 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 1.000summary(modelo6,rsquare=TRUE,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 1.000
##
## R-Square:
## Estimate
## x1 0.596
## x2 0.179
## x3 0.338
## x4 0.725
## x5 0.731
## x6 0.702
## x7 0.324
## x8 0.523
## x9 0.442inspect(modelo6, 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 1.000fitMeasures(modelo6)## npar fmin chisq
## 21.000 0.142 85.306
## df pvalue baseline.chisq
## 24.000 0.000 918.852
## baseline.df baseline.pvalue cfi
## 36.000 0.000 0.931
## tli nnfi rfi
## 0.896 0.896 0.861
## nfi pnfi ifi
## 0.907 0.605 0.931
## rni logl unrestricted.logl
## 0.931 -3737.745 -3695.092
## aic bic ntotal
## 7517.490 7595.339 301.000
## bic2 rmsea rmsea.ci.lower
## 7528.739 0.092 0.071
## rmsea.ci.upper rmsea.ci.level rmsea.pvalue
## 0.114 0.900 0.001
## rmsea.close.h0 rmsea.notclose.pvalue rmsea.notclose.h0
## 0.050 0.840 0.080
## rmr rmr_nomean srmr
## 0.082 0.082 0.065
## srmr_bentler srmr_bentler_nomean crmr
## 0.065 0.065 0.073
## crmr_nomean srmr_mplus srmr_mplus_nomean
## 0.073 0.065 0.065
## cn_05 cn_01 gfi
## 129.490 152.654 0.943
## agfi pgfi mfi
## 0.894 0.503 0.903
## ecvi
## 0.423fitMeasures( modelo6, c( "rmr","rmsea","gfi","agfi", "nfi","cfi" ) )## rmr rmsea gfi agfi nfi cfi
## 0.082 0.092 0.943 0.894 0.907 0.931param<- parameterestimates(modelo6, standardized=TRUE );param## lhs op rhs est se z pvalue ci.lower ci.upper std.lv
## 1 visual =~ x1 1.000 0.000 NA NA 1.000 1.000 0.900
## 2 visual =~ x2 0.554 0.100 5.554 0 0.358 0.749 0.498
## 3 visual =~ x3 0.729 0.109 6.685 0 0.516 0.943 0.656
## 4 textual =~ x4 1.000 0.000 NA NA 1.000 1.000 0.990
## 5 textual =~ x5 1.113 0.065 17.014 0 0.985 1.241 1.102
## 6 textual =~ x6 0.926 0.055 16.703 0 0.817 1.035 0.917
## 7 speed =~ x7 1.000 0.000 NA NA 1.000 1.000 0.619
## 8 speed =~ x8 1.180 0.165 7.152 0 0.857 1.503 0.731
## 9 speed =~ x9 1.082 0.151 7.155 0 0.785 1.378 0.670
## 10 x1 ~~ x1 0.549 0.114 4.833 0 0.326 0.772 0.549
## 11 x2 ~~ x2 1.134 0.102 11.146 0 0.934 1.333 1.134
## 12 x3 ~~ x3 0.844 0.091 9.317 0 0.667 1.022 0.844
## 13 x4 ~~ x4 0.371 0.048 7.779 0 0.278 0.465 0.371
## 14 x5 ~~ x5 0.446 0.058 7.642 0 0.332 0.561 0.446
## 15 x6 ~~ x6 0.356 0.043 8.277 0 0.272 0.441 0.356
## 16 x7 ~~ x7 0.799 0.081 9.823 0 0.640 0.959 0.799
## 17 x8 ~~ x8 0.488 0.074 6.573 0 0.342 0.633 0.488
## 18 x9 ~~ x9 0.566 0.071 8.003 0 0.427 0.705 0.566
## 19 visual ~~ visual 0.809 0.145 5.564 0 0.524 1.094 1.000
## 20 textual ~~ textual 0.979 0.112 8.737 0 0.760 1.199 1.000
## 21 speed ~~ speed 0.384 0.086 4.451 0 0.215 0.553 1.000
## 22 visual ~~ textual 0.408 0.074 5.552 0 0.264 0.552 0.459
## 23 visual ~~ speed 0.262 0.056 4.660 0 0.152 0.373 0.471
## 24 textual ~~ speed 0.173 0.049 3.518 0 0.077 0.270 0.283
## std.all std.nox
## 1 0.772 0.772
## 2 0.424 0.424
## 3 0.581 0.581
## 4 0.852 0.852
## 5 0.855 0.855
## 6 0.838 0.838
## 7 0.570 0.570
## 8 0.723 0.723
## 9 0.665 0.665
## 10 0.404 0.404
## 11 0.821 0.821
## 12 0.662 0.662
## 13 0.275 0.275
## 14 0.269 0.269
## 15 0.298 0.298
## 16 0.676 0.676
## 17 0.477 0.477
## 18 0.558 0.558
## 19 1.000 1.000
## 20 1.000 1.000
## 21 1.000 1.000
## 22 0.459 0.459
## 23 0.471 0.471
## 24 0.283 0.283semPaths(modelo6, intAtSide=TRUE)
semPaths(modelo6,"std","hide", intAtSide=TRUE)
semPaths(modelo6,'std', 'est', curveAdjacent = TRUE, style = "lisrel")
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O.M.F.
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paquetes utilizados:
polycor, ggcorrplot
GPArotation, lavaan
tidyverse,semTools
semPlot,psych
MVN
diagram
lavaanPlot
piecewiseSEM
corrr
corrplot