Análise Fatorial Confirmatórica com Lavan
Ricardo Primi
23 de abril de 2018
Bibliotecas
library(knitr)
library(semPlot)
library(tidyverse)Exemplo do Cap 3 do livro de (Beaujean, 2014)
#### Dados
# Ative o lavaan
library(lavaan)
# Cria uma matriz de correlação
wisc4.cor <- lav_matrix_lower2full(c(1,0.72,1,0.64,0.63,1,0.51,0.48,0.37,1,0.37,0.38,0.38,0.38,1))
# Cria vetor com desvios padr
wisc4.sd <- c(3.01 , 3.03 , 2.99 , 2.89 , 2.98)
# nomeia variáveis
colnames(wisc4.cor) <- rownames(wisc4.cor) <- c("Information", "Similarities",
"Word.Reasoning", "Matrix.Reasoning", "Picture.Concepts")
names(wisc4.sd) <- c("Information", "Similarities", "Word.Reasoning", "Matrix.Reasoning",
"Picture.Concepts")
# Converte matriz de correlação em covariâncias
wisc4.cov <- cor2cov(wisc4.cor,wisc4.sd)
wisc4.cor %>% kable(digits = 2)| Information | Similarities | Word.Reasoning | Matrix.Reasoning | Picture.Concepts | |
|---|---|---|---|---|---|
| Information | 1.00 | 0.72 | 0.64 | 0.51 | 0.37 |
| Similarities | 0.72 | 1.00 | 0.63 | 0.48 | 0.38 |
| Word.Reasoning | 0.64 | 0.63 | 1.00 | 0.37 | 0.38 |
| Matrix.Reasoning | 0.51 | 0.48 | 0.37 | 1.00 | 0.38 |
| Picture.Concepts | 0.37 | 0.38 | 0.38 | 0.38 | 1.00 |
wisc4.cov %>% kable(digits = 2)| Information | Similarities | Word.Reasoning | Matrix.Reasoning | Picture.Concepts | |
|---|---|---|---|---|---|
| Information | 9.06 | 6.57 | 5.76 | 4.44 | 3.32 |
| Similarities | 6.57 | 9.18 | 5.71 | 4.20 | 3.43 |
| Word.Reasoning | 5.76 | 5.71 | 8.94 | 3.20 | 3.39 |
| Matrix.Reasoning | 4.44 | 4.20 | 3.20 | 8.35 | 3.27 |
| Picture.Concepts | 3.32 | 3.43 | 3.39 | 3.27 | 8.88 |
| #### Estimação do m | odelo e result | ados |
# Especifica modelo
wisc4.model<-"
g =~ a*Information + b*Similarities + c*Word.Reasoning + d*Matrix.Reasoning +
e*Picture.Concepts
"
# Roda o modelo
wisc4.fit <- cfa(model=wisc4.model, sample.cov=wisc4.cov, sample.nobs=550, std.lv=FALSE)
# Examina resultados
summary(wisc4.fit,standardized=TRUE)## lavaan (0.5-23.1097) converged normally after 30 iterations
##
## Number of observations 550
##
## Estimator ML
## Minimum Function Test Statistic 26.775
## Degrees of freedom 5
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## g =~
## Informatin (a) 1.000 2.578 0.857
## Similarits (b) 0.985 0.045 21.708 0.000 2.541 0.839
## Word.Rsnng (c) 0.860 0.045 18.952 0.000 2.217 0.742
## Mtrx.Rsnng (d) 0.647 0.047 13.896 0.000 1.669 0.578
## Pctr.Cncpt (e) 0.542 0.050 10.937 0.000 1.398 0.470
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Information 2.395 0.250 9.587 0.000 2.395 0.265
## .Similarities 2.709 0.258 10.482 0.000 2.709 0.296
## .Word.Reasoning 4.009 0.295 13.600 0.000 4.009 0.449
## .Matrix.Reasnng 5.551 0.360 15.400 0.000 5.551 0.666
## .Picture.Cncpts 6.909 0.434 15.922 0.000 6.909 0.779
## g 6.648 0.564 11.788 0.000 1.000 1.000 parameterEstimates(wisc4.fit,standardized=TRUE)## lhs op rhs label est se z pvalue
## 1 g =~ Information a 1.000 0.000 NA NA
## 2 g =~ Similarities b 0.985 0.045 21.708 0
## 3 g =~ Word.Reasoning c 0.860 0.045 18.952 0
## 4 g =~ Matrix.Reasoning d 0.647 0.047 13.896 0
## 5 g =~ Picture.Concepts e 0.542 0.050 10.937 0
## 6 Information ~~ Information 2.395 0.250 9.587 0
## 7 Similarities ~~ Similarities 2.709 0.258 10.482 0
## 8 Word.Reasoning ~~ Word.Reasoning 4.009 0.295 13.600 0
## 9 Matrix.Reasoning ~~ Matrix.Reasoning 5.551 0.360 15.400 0
## 10 Picture.Concepts ~~ Picture.Concepts 6.909 0.434 15.922 0
## 11 g ~~ g 6.648 0.564 11.788 0
## ci.lower ci.upper std.lv std.all std.nox
## 1 1.000 1.000 2.578 0.857 0.857
## 2 0.896 1.074 2.541 0.839 0.839
## 3 0.771 0.949 2.217 0.742 0.742
## 4 0.556 0.739 1.669 0.578 0.578
## 5 0.445 0.640 1.398 0.470 0.470
## 6 1.906 2.885 2.395 0.265 0.265
## 7 2.202 3.215 2.709 0.296 0.296
## 8 3.431 4.587 4.009 0.449 0.449
## 9 4.845 6.258 5.551 0.666 0.666
## 10 6.058 7.759 6.909 0.779 0.779
## 11 5.543 7.754 1.000 1.000 1.000# Covariâncias implicadas pelo modelo
fitted(wisc4.fit)## $cov
## Infrmt Smlrts Wrd.Rs Mtrx.R Pctr.C
## Information 9.044
## Similarities 6.551 9.164
## Word.Reasoning 5.716 5.633 8.924
## Matrix.Reasoning 4.303 4.241 3.700 8.337
## Picture.Concepts 3.606 3.553 3.100 2.334 8.864
##
## $mean
## Information Similarities Word.Reasoning Matrix.Reasoning
## 0 0 0 0
## Picture.Concepts
## 0# Transforma Covariâncias implicadas pelo modelo em correlaçòes
wisc4Fit.cov <- fitted(wisc4.fit)$cov
wisc4Fit.cor <- cov2cor(wisc4Fit.cov)
# Resíduos
residuals(wisc4.fit,type="cor")## $type
## [1] "cor.bollen"
##
## $cor
## Infrmt Smlrts Wrd.Rs Mtrx.R Pctr.C
## Information 0.000
## Similarities 0.000 0.000
## Word.Reasoning 0.004 0.007 0.000
## Matrix.Reasoning 0.014 -0.005 -0.059 0.000
## Picture.Concepts -0.033 -0.014 0.031 0.109 0.000
##
## $mean
## Information Similarities Word.Reasoning Matrix.Reasoning
## 0 0 0 0
## Picture.Concepts
## 0# Medidas de ajuste do modelo
fitMeasures(wisc4.fit)## npar fmin chisq
## 10.000 0.024 26.775
## df pvalue baseline.chisq
## 5.000 0.000 1073.427
## baseline.df baseline.pvalue cfi
## 10.000 0.000 0.980
## tli nnfi rfi
## 0.959 0.959 0.950
## nfi pnfi ifi
## 0.975 0.488 0.980
## rni logl unrestricted.logl
## 0.980 -6378.678 -6365.291
## aic bic ntotal
## 12777.357 12820.456 550.000
## bic2 rmsea rmsea.ci.lower
## 12788.712 0.089 0.058
## rmsea.ci.upper rmsea.pvalue rmr
## 0.123 0.022 0.298
## rmr_nomean srmr srmr_bentler
## 0.298 0.034 0.034
## srmr_bentler_nomean srmr_bollen srmr_bollen_nomean
## 0.034 0.034 0.034
## srmr_mplus srmr_mplus_nomean cn_05
## 0.034 0.034 228.408
## cn_01 gfi agfi
## 310.899 0.982 0.947
## pgfi mfi ecvi
## 0.327 0.980 0.085# Indices de modoficação
modificationIndices(wisc4.fit) ## lhs op rhs mi epc sepc.lv sepc.all
## 12 Information ~~ Similarities 0.010 0.034 0.034 0.004
## 13 Information ~~ Word.Reasoning 0.279 0.147 0.147 0.016
## 14 Information ~~ Matrix.Reasoning 1.447 0.280 0.280 0.032
## 15 Information ~~ Picture.Concepts 5.493 -0.565 -0.565 -0.063
## 16 Similarities ~~ Word.Reasoning 0.791 0.242 0.242 0.027
## 17 Similarities ~~ Matrix.Reasoning 0.147 -0.089 -0.089 -0.010
## 18 Similarities ~~ Picture.Concepts 0.838 -0.223 -0.223 -0.025
## 19 Word.Reasoning ~~ Matrix.Reasoning 8.931 -0.710 -0.710 -0.082
## 20 Word.Reasoning ~~ Picture.Concepts 2.029 0.365 0.365 0.041
## 21 Matrix.Reasoning ~~ Picture.Concepts 14.157 1.058 1.058 0.123
## sepc.nox
## 12 0.004
## 13 0.016
## 14 0.032
## 15 -0.063
## 16 0.027
## 17 -0.010
## 18 -0.025
## 19 -0.082
## 20 0.041
## 21 0.123Exercício
- Modifique o modelo para dois fatores e rode novamente
- Procure um artigo de seu interesse em que ha uma matriz de correlação publicada. Com essa matriz crie um modelo e rode a análise CFA
Referências
Beaujean, A. A. (2014). Latent Variable Modeling Using R: A Step-By-Step Guide (Edição: 1.). New York: Routledge.