Análise Fatorial Confirmatória
Daniel Lopes
24 de abril de 2019
Carregando pacotes
#Pacote Alpha Cronbach
library(psych)
#Pacotes para CFA
library(lavaan)
library(semTools)
library(semPlot)Carregando a base de dados
data.cfa <- read.csv2("C:/Users/Daniel/Desktop/Projetos/CFA/cfa.csv")
head(data.cfa)## COM1 COM2 COM3 COM4 DED1 DED2 DED3 DED4 BEN1 BEN2 BEN3 BEN4
## 1 4 5 4 5 5 3 5 5 5 5 3 5
## 2 2 2 1 4 5 4 4 4 5 5 2 5
## 3 2 2 2 4 2 1 2 4 5 5 3 4
## 4 5 5 5 5 5 5 5 5 5 5 5 5
## 5 5 5 5 3 5 4 5 5 4 5 2 5
## 6 5 5 4 5 3 5 5 3 5 5 3 5Os dados incluem quatro itens para cada dimensão de Competência, Dedicação e Benevolência. Estas três dimensões constituem o constructo de trustworthiness, segundo Nooteboom (2002).
data.cfa$comtotal <- (data.cfa$COM1 + data.cfa$COM2 + data.cfa$COM3 + data.cfa$COM4) / 4
cor(data.cfa[1:4], data.cfa[13])## comtotal
## COM1 0.8952040
## COM2 0.7607075
## COM3 0.8190807
## COM4 0.7128979data.cfa$dedtotal <- (data.cfa$DED1 + data.cfa$DED2 + data.cfa$DED3 + data.cfa$DED4) / 4
cor(data.cfa[5:8], data.cfa[14])## dedtotal
## DED1 0.8915662
## DED2 0.7607183
## DED3 0.8408274
## DED4 0.8879951data.cfa$bentotal <- (data.cfa$BEN1 + data.cfa$BEN2 + data.cfa$BEN3 + data.cfa$BEN4) / 4
cor(data.cfa[9:12], data.cfa[15])## bentotal
## BEN1 0.5130898
## BEN2 0.6990352
## BEN3 0.6832269
## BEN4 0.7805646pairs(data.cfa[13:15])
Alpha de Cronbach
cronbachalpha.cfa <- data.frame(data.cfa[1:12])
alpha(cronbachalpha.cfa)##
## Reliability analysis
## Call: alpha(x = cronbachalpha.cfa)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.89 0.89 0.91 0.4 8.1 0.011 3.5 0.87 0.39
##
## lower alpha upper 95% confidence boundaries
## 0.87 0.89 0.91
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## COM1 0.87 0.87 0.89 0.39 7.0 0.013 0.033 0.38
## COM2 0.89 0.89 0.91 0.43 8.2 0.011 0.031 0.42
## COM3 0.87 0.88 0.90 0.39 7.0 0.013 0.035 0.38
## COM4 0.88 0.89 0.91 0.42 7.9 0.012 0.038 0.42
## DED1 0.87 0.87 0.89 0.38 6.7 0.014 0.031 0.38
## DED2 0.88 0.88 0.90 0.41 7.5 0.012 0.038 0.38
## DED3 0.87 0.87 0.89 0.38 6.9 0.013 0.033 0.38
## DED4 0.87 0.87 0.89 0.38 6.8 0.013 0.033 0.38
## BEN1 0.89 0.90 0.91 0.44 8.6 0.011 0.033 0.44
## BEN2 0.90 0.90 0.91 0.44 8.8 0.010 0.028 0.44
## BEN3 0.88 0.88 0.91 0.41 7.6 0.012 0.036 0.39
## BEN4 0.87 0.87 0.89 0.39 6.9 0.013 0.033 0.38
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## COM1 200 0.78 0.78 0.78 0.73 3.2 1.33
## COM2 200 0.52 0.52 0.47 0.42 3.4 1.40
## COM3 200 0.78 0.77 0.76 0.72 2.9 1.38
## COM4 200 0.58 0.59 0.53 0.50 3.7 1.27
## DED1 200 0.85 0.85 0.85 0.81 3.3 1.40
## DED2 200 0.68 0.66 0.62 0.59 2.8 1.44
## DED3 200 0.80 0.81 0.80 0.76 3.7 1.24
## DED4 200 0.82 0.82 0.82 0.77 3.5 1.39
## BEN1 200 0.39 0.44 0.36 0.33 4.7 0.74
## BEN2 200 0.43 0.41 0.33 0.29 3.7 1.59
## BEN3 200 0.64 0.65 0.60 0.57 2.9 1.16
## BEN4 200 0.78 0.79 0.79 0.73 3.8 1.15
##
## Non missing response frequency for each item
## 1 2 3 4 5 miss
## COM1 0.12 0.25 0.18 0.25 0.20 0
## COM2 0.12 0.18 0.19 0.20 0.30 0
## COM3 0.18 0.30 0.15 0.20 0.18 0
## COM4 0.06 0.16 0.14 0.28 0.36 0
## DED1 0.13 0.18 0.22 0.18 0.30 0
## DED2 0.24 0.24 0.23 0.08 0.20 0
## DED3 0.06 0.14 0.16 0.30 0.34 0
## DED4 0.10 0.20 0.14 0.22 0.33 0
## BEN1 0.00 0.02 0.08 0.09 0.80 0
## BEN2 0.19 0.06 0.14 0.08 0.53 0
## BEN3 0.16 0.14 0.46 0.12 0.10 0
## BEN4 0.04 0.08 0.22 0.27 0.38 0Análise Fatorial Confirmatória
Especificando o modelo e estimando os parâmetros
mod_lat <- '
lat_COM =~ COM1 + COM2 + COM3 + COM4
lat_DED =~ DED1 + DED2 + DED3 + DED4
lat_BEN =~ BEN1 + BEN2 + BEN3 + BEN4
'
mod_lat_fit <- cfa(mod_lat, data=data.cfa, std.lv=FALSE)
summary(mod_lat_fit, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE) ## lavaan 0.6-3 ended normally after 53 iterations
##
## Optimization method NLMINB
## Number of free parameters 27
##
## Number of observations 200
##
## Estimator ML
## Model Fit Test Statistic 134.161
## Degrees of freedom 51
## P-value (Chi-square) 0.000
##
## Model test baseline model:
##
## Minimum Function Test Statistic 1312.805
## Degrees of freedom 66
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.933
## Tucker-Lewis Index (TLI) 0.914
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3382.695
## Loglikelihood unrestricted model (H1) -3315.614
##
## Number of free parameters 27
## Akaike (AIC) 6819.389
## Bayesian (BIC) 6908.444
## Sample-size adjusted Bayesian (BIC) 6822.905
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.090
## 90 Percent Confidence Interval 0.072 0.109
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.061
##
## Parameter Estimates:
##
## Information Expected
## Information saturated (h1) model Structured
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## lat_COM =~
## COM1 1.000 1.216 0.918
## COM2 0.709 0.074 9.587 0.000 0.862 0.619
## COM3 0.906 0.066 13.681 0.000 1.101 0.801
## COM4 0.583 0.069 8.457 0.000 0.709 0.562
## lat_DED =~
## DED1 1.000 1.240 0.890
## DED2 0.676 0.074 9.170 0.000 0.839 0.586
## DED3 0.823 0.053 15.448 0.000 1.020 0.823
## DED4 0.956 0.057 16.652 0.000 1.186 0.856
## lat_BEN =~
## BEN1 1.000 0.266 0.362
## BEN2 2.112 0.580 3.641 0.000 0.562 0.353
## BEN3 2.781 0.588 4.732 0.000 0.740 0.641
## BEN4 3.642 0.721 5.051 0.000 0.969 0.843
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## lat_COM ~~
## lat_DED 1.133 0.149 7.585 0.000 0.751 0.751
## lat_BEN 0.228 0.054 4.256 0.000 0.705 0.705
## lat_DED ~~
## lat_BEN 0.322 0.071 4.536 0.000 0.975 0.975
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .COM1 0.275 0.071 3.901 0.000 0.275 0.157
## .COM2 1.194 0.129 9.284 0.000 1.194 0.616
## .COM3 0.679 0.089 7.635 0.000 0.679 0.359
## .COM4 1.092 0.115 9.479 0.000 1.092 0.685
## .DED1 0.403 0.058 6.959 0.000 0.403 0.208
## .DED2 1.347 0.140 9.602 0.000 1.347 0.657
## .DED3 0.497 0.059 8.364 0.000 0.497 0.323
## .DED4 0.514 0.066 7.842 0.000 0.514 0.268
## .BEN1 0.469 0.048 9.838 0.000 0.469 0.869
## .BEN2 2.214 0.225 9.847 0.000 2.214 0.875
## .BEN3 0.783 0.086 9.156 0.000 0.783 0.589
## .BEN4 0.382 0.065 5.861 0.000 0.382 0.289
## lat_COM 1.479 0.185 7.993 0.000 1.000 1.000
## lat_DED 1.538 0.194 7.911 0.000 1.000 1.000
## lat_BEN 0.071 0.028 2.524 0.012 1.000 1.000
##
## R-Square:
## Estimate
## COM1 0.843
## COM2 0.384
## COM3 0.641
## COM4 0.315
## DED1 0.792
## DED2 0.343
## DED3 0.677
## DED4 0.732
## BEN1 0.131
## BEN2 0.125
## BEN3 0.411
## BEN4 0.711