Practica de Analisis Factorial
library(haven)
library(ggplot2)
library(MVN)
library(psych)
library(nFactors)
datos = read_sav("Ciencias_Letras.sav")
par(mfrow = c(3, 2))
qqnorm(datos$CNa)
qqline(datos$CNa)
qqnorm(datos$Mat)
qqline(datos$Mat)
qqnorm(datos$Fra)
qqline(datos$Fra)
qqnorm(datos$Lat)
qqline(datos$Lat)
qqnorm(datos$Lit)
qqline(datos$Lit)
shapiro.test(datos$CNa)
##
## Shapiro-Wilk normality test
##
## data: datos$CNa
## W = 0.91452, p-value = 0.07777
shapiro.test(datos$Mat)
##
## Shapiro-Wilk normality test
##
## data: datos$Mat
## W = 0.94253, p-value = 0.2675
shapiro.test(datos$Fra)
##
## Shapiro-Wilk normality test
##
## data: datos$Fra
## W = 0.91746, p-value = 0.08855
shapiro.test(datos$Lat)
##
## Shapiro-Wilk normality test
##
## data: datos$Lat
## W = 0.92895, p-value = 0.1474
shapiro.test(datos$Lit)
##
## Shapiro-Wilk normality test
##
## data: datos$Lit
## W = 0.90352, p-value = 0.04803
fit.ml = fa(datos[, 2:6], nfactors = 2, fm = "ml", rotate = "none", n.obs = 220, scores = "regression")
print(fit.ml)
## Factor Analysis using method = ml
## Call: fa(r = datos[, 2:6], nfactors = 2, n.obs = 220, rotate = "none",
## scores = "regression", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML2 ML1 h2 u2 com
## CNa 0.42 0.67 0.62 0.378 1.7
## Mat -0.03 1.00 1.00 0.005 1.0
## Fra 0.97 0.13 0.96 0.040 1.0
## Lat 0.80 0.25 0.71 0.291 1.2
## Lit 0.82 0.34 0.79 0.205 1.3
##
## ML2 ML1
## SS loadings 2.44 1.64
## Proportion Var 0.49 0.33
## Cumulative Var 0.49 0.82
## Proportion Explained 0.60 0.40
## Cumulative Proportion 0.60 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 10 and the objective function was 3.66 with Chi Square of 60.31
## The degrees of freedom for the model are 1 and the objective function was 0.08
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.09
##
## The harmonic number of observations is 20 with the empirical chi square 0.3 with prob < 0.58
## The total number of observations was 20 with Likelihood Chi Square = 1.23 with prob < 0.27
##
## Tucker Lewis Index of factoring reliability = 0.95
## RMSEA index = 0.093 and the 90 % confidence intervals are 0 0.631
## BIC = -1.77
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## ML2 ML1
## Correlation of (regression) scores with factors 0.98 1.00
## Multiple R square of scores with factors 0.97 1.00
## Minimum correlation of possible factor scores 0.94 0.99
ev = eigen(cor(datos[, 2:6])) # Obtencion de los autovalores.
ap = parallel(subject = nrow(datos[, 2:6]),
var = ncol(datos[, 2:6]),
rep = 100,
cent = 0.05)
nS = nScree(x = ev$values, aparallel = ap$eigen$qevpea)
plotnScree(nS, xlab = "Numero de Componentes", ylab = "Autovalores",
main = "Solucion por autovalores para determinar \n el numero de factores o componentes")
fit.pa.rot.vari = fa(datos[, 2:6],
nfactors = 2,
fm = "pa",
rotate = "varimax",
n.obs = 220,
scores = "regression")
## maximum iteration exceeded
fit.pa.rot.vari
## Factor Analysis using method = pa
## Call: fa(r = datos[, 2:6], nfactors = 2, n.obs = 220, rotate = "varimax",
## scores = "regression", fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 h2 u2 com
## CNa 0.42 0.68 0.64 0.357 1.7
## Mat 0.04 0.93 0.88 0.124 1.0
## Fra 0.98 0.08 0.96 0.038 1.0
## Lat 0.81 0.18 0.69 0.307 1.1
## Lit 0.85 0.31 0.82 0.175 1.3
##
## PA1 PA2
## SS loadings 2.53 1.47
## Proportion Var 0.51 0.29
## Cumulative Var 0.51 0.80
## Proportion Explained 0.63 0.37
## Cumulative Proportion 0.63 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 10 and the objective function was 3.66 with Chi Square of 60.31
## The degrees of freedom for the model are 1 and the objective function was 0.11
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.07
##
## The harmonic number of observations is 20 with the empirical chi square 0.19 with prob < 0.66
## The total number of observations was 20 with Likelihood Chi Square = 1.62 with prob < 0.2
##
## Tucker Lewis Index of factoring reliability = 0.863
## RMSEA index = 0.169 and the 90 % confidence intervals are 0 0.67
## BIC = -1.37
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2
## Correlation of (regression) scores with factors 0.98 0.94
## Multiple R square of scores with factors 0.97 0.89
## Minimum correlation of possible factor scores 0.94 0.78
fit.pa.rot.qua = fa(datos[, 2:6],
nfactors = 2,
fm = "pa",
rotate = "quartimax",
n.obs = 220,
scores = "regression")
## maximum iteration exceeded
## Loading required namespace: GPArotation
fit.pa.rot.qua
## Factor Analysis using method = pa
## Call: fa(r = datos[, 2:6], nfactors = 2, n.obs = 220, rotate = "quartimax",
## scores = "regression", fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 h2 u2 com
## CNa 0.50 0.63 0.64 0.357 1.9
## Mat 0.15 0.92 0.88 0.124 1.0
## Fra 0.98 -0.03 0.96 0.038 1.0
## Lat 0.83 0.09 0.69 0.307 1.0
## Lit 0.88 0.21 0.82 0.175 1.1
##
## PA1 PA2
## SS loadings 2.69 1.30
## Proportion Var 0.54 0.26
## Cumulative Var 0.54 0.80
## Proportion Explained 0.67 0.33
## Cumulative Proportion 0.67 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 10 and the objective function was 3.66 with Chi Square of 60.31
## The degrees of freedom for the model are 1 and the objective function was 0.11
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.07
##
## The harmonic number of observations is 20 with the empirical chi square 0.19 with prob < 0.66
## The total number of observations was 20 with Likelihood Chi Square = 1.62 with prob < 0.2
##
## Tucker Lewis Index of factoring reliability = 0.863
## RMSEA index = 0.169 and the 90 % confidence intervals are 0 0.67
## BIC = -1.37
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2
## Correlation of (regression) scores with factors 0.99 0.94
## Multiple R square of scores with factors 0.97 0.89
## Minimum correlation of possible factor scores 0.95 0.77