Práctico 7. AFE y puntajes factoriales

Estadística IV

Fecha de publicación

16 de octubre de 2024

Análisis factorial exploratorio (AFE)

Presentación

Para el taller práctico de hoy utilizaremos la base de datos del Estudio Longitudinal Social de Chile, realizado por el Centro de estudios del conflicto y la cohesión social COES.

El Estudio Longitudinal Social del Chile ELSOC, único en Chile y América Latina, consiste en encuestar a casi 3.000 chilenos, anualmente, a lo largo de una década. ELSOC ha sido diseñado para evaluar la manera cómo piensan, sienten y se comportan los chilenos en torno a un conjunto de temas referidos al conflicto y la cohesión social en Chile. La población objetivo son hombres y mujeres entre 15 y 75 años de edad, tiene una representación de la población nacional urbana, donde se obtuvo una muestra original de 2927 casos en el año 2016 y mantiene 1728 en 2022, además de una muestra de refresco en 2018.

Objetivo general

El objetivo de este ejercicio práctico es comprender y estimar un análisis factorial exploratorio con el fin de reducir la dimensionalidad de una batería de variables.

Cargar paquetes

Código 
pacman::p_load(tidyverse, #Conjunto de paquetes, sobre todo dplyr y ggplot2
               car, #Para recodificar
               haven,
               summarytools, #Para descriptivos
               sjmisc,
               psych,     # para Alfa de Chronbach
               sjPlot,
               psy, # scree plot function
               nFactors, # parallel
               GPArotation, # Rotación
               sjlabelled)

options(scipen = 999) # para desactivar notacion cientifica
rm(list = ls()) # para limpiar el entorno de trabajo

Cargar base de datos

Código 
load(url("https://dataverse.harvard.edu/api/access/datafile/7245118")) #Cargar base de datos

Visualización de datos

Código 
dim(elsoc_long_2016_2022.2)
[1] 18035   750

Debido a la naturaleza longitudinal de ELSOC, la base de datos contiene 18035 casos (las mismas personas durante 6 años) y 750 variables (las mismas variables en 6 periodos distintos). Por lo tanto, para simplificar el proceso de análisis de este práctico trabajaremos solo con los casos y variables de quienes participaron en la cuarta ola (2019)

Datos y variables

Para estimar AFE, utilizaremos específicamente el módulo de Ciudadanía. De este módulo utilizaremos un concepto en particular llamado Confianza en instituciones con los ítems:

  • Grado de confianza: El Gobierno

  • Grado de confianza: Los Partidos políticos

  • Grado de confianza: Carabineros

  • Grado de confianza: Los sindicatos

  • Grado de confianza: Las empresas privadas

  • Grado de confianza: El congreso nacional

  • Grado de confianza: El presidente de la república

La idea general es ver si esque todas estas variables miden algún tipo de confianza o si esque existen dimensiones subyacentes.

Asimismo, vamos a utilizar los promedios y/o puntajes de estas variables para ver cómo influyen en la Satisfacción con la democracia en Chile

Filtrar base de datos

Filtraremos la base de datos para quedarnos con las observaciones correspondientes solamente a la ola 4, y además seleccionaremos los ítems de interés.

Código 
data <- elsoc_long_2016_2022.2 %>% filter(ola==4) %>%  # seleccionamos solo los casos de la ola 1
  select(satis_dem = c01,
         conf_gob = c05_01,
         conf_part = c05_02,
         conf_carab = c05_03,
         conf_sind = c05_04,
         conf_empre = c05_06,
         conf_cong = c05_07,
         conf_pres = c05_08,
         )

Estos ítems cuentan con las mismas categorías de respuesta: (1) Nada, a (5) Mucho. Además de los valores codificados como -888 y -999.

Recodificar

Recodificamos los valores -888 y -999 en NA y eliminamos los NAs.

Código 
data$satis_dem <- car::recode(data$satis_dem, "c(-999,-888)=NA")
data$conf_gob <- car::recode(data$conf_gob, "c(-999,-888)=NA")
data$conf_part <- car::recode(data$conf_part, "c(-999,-888)=NA")
data$conf_carab <- car::recode(data$conf_carab, "c(-999,-888)=NA")
data$conf_sind <- car::recode(data$conf_sind, "c(-999,-888)=NA")
data$conf_empre <- car::recode(data$conf_empre, "c(-999,-888)=NA")
data$conf_cong <- car::recode(data$conf_cong, "c(-999,-888)=NA")
data$conf_pres <- car::recode(data$conf_pres, "c(-999,-888)=NA")


data$conf_gob <- set_labels(data$conf_gob,
            labels=c( "Nada"=1,
                      "Poca"=2,
                      "Algo"=3,
                      "Bastante"=4,
                      "Mucha"=5))

data$conf_part <- set_labels(data$conf_part,
            labels=c( "Nada"=1,
                      "Poca"=2,
                      "Algo"=3,
                      "Bastante"=4,
                      "Mucha"=5))

data$conf_carab <- set_labels(data$conf_carab,
            labels=c( "Nada"=1,
                      "Poca"=2,
                      "Algo"=3,
                      "Bastante"=4,
                      "Mucha"=5))

data$conf_sind <- set_labels(data$conf_sind,
            labels=c( "Nada"=1,
                      "Poca"=2,
                      "Algo"=3,
                      "Bastante"=4,
                      "Mucha"=5))
data$conf_empre <- set_labels(data$conf_empre,
            labels=c( "Nada"=1,
                      "Poca"=2,
                      "Algo"=3,
                      "Bastante"=4,
                      "Mucha"=5))
data$conf_cong <- set_labels(data$conf_cong,
            labels=c( "Nada"=1,
                      "Poca"=2,
                      "Algo"=3,
                      "Bastante"=4,
                      "Mucha"=5))
data$conf_pres <- set_labels(data$conf_pres,
            labels=c( "Nada"=1,
                      "Poca"=2,
                      "Algo"=3,
                      "Bastante"=4,
                      "Mucha"=5))

Análisis

Código 
data %>% select(conf_gob:conf_pres) %>% 
  plot_stackfrq() + theme(legend.position="bottom")

Estimar correlación

Código 
data %>% select(conf_gob:conf_pres) %>% tab_corr(triangle = "lower")
  Grado de confianza: El Gobierno Grado de confianza: Los Partidos
Politicos		 Grado de confianza: Carabineros Grado de confianza: Los Sindicatos Grado de confianza: Las Empresas
Privadas		 Grado de confianza: El Congreso Nacional Grado de confianza: El Presidente/a de
la Republica
Grado de confianza: El Gobierno              
Grado de confianza: Los Partidos
Politicos		 0.451***            
Grado de confianza: Carabineros 0.517*** 0.232***          
Grado de confianza: Los Sindicatos 0.175*** 0.280*** 0.201***        
Grado de confianza: Las Empresas
Privadas		 0.417*** 0.291*** 0.409*** 0.317***      
Grado de confianza: El Congreso Nacional 0.470*** 0.523*** 0.321*** 0.331*** 0.450***    
Grado de confianza: El Presidente/a de
la Republica		 0.719*** 0.355*** 0.524*** 0.127*** 0.378*** 0.442***  
Computed correlation used pearson-method with listwise-deletion.

Podemos observar que todas las correlaciones son positivas, por lo que no quedaron ítems invertidos.

Código 
data %>% select(conf_gob:conf_pres) %>% psych::alpha()

Reliability analysis   
Call: psych::alpha(x = .)

  raw_alpha std.alpha G6(smc) average_r S/N    ase mean   sd median_r
      0.79      0.81    0.81      0.38 4.2 0.0055  1.8 0.63     0.37

    95% confidence boundaries 
         lower alpha upper
Feldt     0.78  0.79   0.8
Duhachek  0.78  0.79   0.8

 Reliability if an item is dropped:
           raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
conf_gob        0.73      0.76    0.75      0.34 3.1   0.0070 0.013  0.33
conf_part       0.77      0.79    0.79      0.38 3.8   0.0060 0.023  0.41
conf_carab      0.76      0.79    0.79      0.38 3.7   0.0064 0.021  0.37
conf_sind       0.80      0.82    0.82      0.43 4.5   0.0049 0.014  0.44
conf_empre      0.75      0.78    0.79      0.38 3.6   0.0064 0.026  0.35
conf_cong       0.75      0.77    0.77      0.36 3.3   0.0064 0.024  0.35
conf_pres       0.74      0.77    0.76      0.36 3.3   0.0068 0.012  0.33

 Item statistics 
              n raw.r std.r r.cor r.drop mean   sd
conf_gob   3405  0.78  0.78  0.77   0.67  1.6 0.87
conf_part  3394  0.58  0.65  0.57   0.48  1.3 0.57
conf_carab 3409  0.73  0.67  0.59   0.54  2.4 1.25
conf_sind  3253  0.53  0.51  0.37   0.31  2.1 1.09
conf_empre 3339  0.69  0.68  0.59   0.55  1.9 0.97
conf_cong  3382  0.70  0.74  0.69   0.59  1.4 0.71
conf_pres  3399  0.75  0.74  0.72   0.62  1.6 0.92

Non missing response frequency for each item
              1    2    3    4    5 miss
conf_gob   0.60 0.24 0.13 0.03 0.01 0.00
conf_part  0.79 0.16 0.04 0.01 0.00 0.01
conf_carab 0.32 0.23 0.23 0.15 0.07 0.00
conf_sind  0.42 0.23 0.25 0.09 0.02 0.05
conf_empre 0.45 0.28 0.21 0.05 0.01 0.02
conf_cong  0.68 0.21 0.09 0.01 0.00 0.01
conf_pres  0.65 0.18 0.12 0.03 0.01 0.01

Si sacamos conf_sind el alpha sube a 0.8

Código 
data %>% select(conf_gob:conf_carab, conf_empre:conf_pres) %>% psych::alpha()

Reliability analysis   
Call: psych::alpha(x = .)

  raw_alpha std.alpha G6(smc) average_r S/N    ase mean   sd median_r
       0.8      0.82    0.82      0.43 4.5 0.0049  1.7 0.65     0.44

    95% confidence boundaries 
         lower alpha upper
Feldt     0.79   0.8  0.81
Duhachek  0.79   0.8  0.81

 Reliability if an item is dropped:
           raw_alpha std.alpha G6(smc) average_r S/N alpha se  var.r med.r
conf_gob        0.74      0.76    0.74      0.39 3.2   0.0066 0.0089  0.39
conf_part       0.80      0.81    0.80      0.46 4.3   0.0053 0.0118  0.44
conf_carab      0.79      0.80    0.79      0.45 4.0   0.0055 0.0136  0.44
conf_empre      0.79      0.81    0.80      0.45 4.2   0.0054 0.0178  0.46
conf_cong       0.78      0.79    0.77      0.43 3.7   0.0056 0.0187  0.41
conf_pres       0.75      0.77    0.75      0.41 3.4   0.0065 0.0089  0.43

 Item statistics 
              n raw.r std.r r.cor r.drop mean   sd
conf_gob   3405  0.82  0.82  0.80   0.71  1.6 0.87
conf_part  3394  0.57  0.65  0.55   0.46  1.3 0.57
conf_carab 3409  0.76  0.69  0.60   0.56  2.4 1.25
conf_empre 3339  0.69  0.67  0.56   0.51  1.9 0.97
conf_cong  3382  0.69  0.74  0.66   0.57  1.4 0.71
conf_pres  3399  0.80  0.78  0.76   0.68  1.6 0.92

Non missing response frequency for each item
              1    2    3    4    5 miss
conf_gob   0.60 0.24 0.13 0.03 0.01 0.00
conf_part  0.79 0.16 0.04 0.01 0.00 0.01
conf_carab 0.32 0.23 0.23 0.15 0.07 0.00
conf_empre 0.45 0.28 0.21 0.05 0.01 0.02
conf_cong  0.68 0.21 0.09 0.01 0.00 0.01
conf_pres  0.65 0.18 0.12 0.03 0.01 0.01
Código 
data <- cbind(data, 
              "conf_inst"=rowMeans(data %>%
              dplyr::select(conf_gob:conf_carab, conf_empre:conf_pres), 
              na.rm=TRUE))

summary(data$conf_inst)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
  1.000   1.167   1.500   1.700   2.167   5.000       6

Análisis factorial exploratorio

¿Qué se puede deducir de la matriz de correlaciones en relación a la estructura subyacente en términos de variables latentes? No hay claridad de grupos de indicadores asociados entre sí.

Test de adecuación de matriz para AFE

KMO (Kaiser, Meyer, Olkin Measure of Sampling Adequacy):

  • Varía entre 0 y 1. Contrasta si las correlaciones parciales entre las variables son pequeñas

  • Valores pequeños (menores a 0.5) indican que los datos no serían adecuados para AFE, ya que las correlaciones entre pares de variables no pueden ser explicadas por otras variables.

Código 
corMat  <- data %>% select(conf_gob:conf_pres) %>%
  cor(use = "complete.obs")  # estimar matriz pearson

KMO(corMat)
Kaiser-Meyer-Olkin factor adequacy
Call: KMO(r = corMat)
Overall MSA =  0.81
MSA for each item = 
  conf_gob  conf_part conf_carab  conf_sind conf_empre  conf_cong  conf_pres 
      0.78       0.81       0.86       0.80       0.86       0.83       0.77

En este caso las correlaciones son altas, por lo que los datos sí son adecuados para AFE.

Nivel de correlaciones de la matriz: test de esfericidad de Barlett

Se utiliza para evluar la hipótesis que la matriz de correlaciones es una matriz identidad (diagonal=1 y bajo la diagonal=0)

  • Se busca significación (p < 0.05) ya que se espera que las variables estén correlacionadas
Código 
cortest.bartlett(corMat, n = 3417)
$chisq
[1] 7942.816

$p.value
[1] 0

$df
[1] 21

En este caso el valor p es 0, así que hay significación estadística

Selección de número de factores

Código 
data %>% select(conf_gob:conf_pres) %>% scree.plot()

Código 
fa.parallel(corMat, n.obs=3417)

Parallel analysis suggests that the number of factors =  3  and the number of components =  2

Extracción

  • ejes principales
Código 
fac_pa <- data %>% select(conf_gob:conf_pres) %>% fa(nfactors = 3, fm= "pa")
#summary(fac_pa)
fac_pa
Factor Analysis using method =  pa
Call: fa(r = ., nfactors = 3, fm = "pa")
Standardized loadings (pattern matrix) based upon correlation matrix
             PA1   PA2   PA3   h2   u2 com
conf_gob    0.77  0.14  0.00 0.72 0.28 1.1
conf_part   0.07  0.72 -0.04 0.55 0.45 1.0
conf_carab  0.52 -0.13  0.32 0.45 0.55 1.8
conf_sind  -0.19  0.29  0.42 0.27 0.73 2.2
conf_empre  0.14  0.07  0.59 0.50 0.50 1.1
conf_cong   0.12  0.53  0.23 0.55 0.45 1.5
conf_pres   0.87  0.00 -0.02 0.74 0.26 1.0

                       PA1  PA2  PA3
SS loadings           1.84 1.08 0.87
Proportion Var        0.26 0.15 0.12
Cumulative Var        0.26 0.42 0.54
Proportion Explained  0.48 0.29 0.23
Cumulative Proportion 0.48 0.77 1.00

 With factor correlations of 
     PA1  PA2  PA3
PA1 1.00 0.51 0.48
PA2 0.51 1.00 0.44
PA3 0.48 0.44 1.00

Mean item complexity =  1.4
Test of the hypothesis that 3 factors are sufficient.

df null model =  21  with the objective function =  2.3 with Chi Square =  7858.1
df of  the model are 3  and the objective function was  0.01 

The root mean square of the residuals (RMSR) is  0.01 
The df corrected root mean square of the residuals is  0.03 

The harmonic n.obs is  3337 with the empirical chi square  12.76  with prob <  0.0052 
The total n.obs was  3417  with Likelihood Chi Square =  39.13  with prob <  0.000000016 

Tucker Lewis Index of factoring reliability =  0.968
RMSEA index =  0.059  and the 90 % confidence intervals are  0.044 0.077
BIC =  14.72
Fit based upon off diagonal values = 1
Measures of factor score adequacy             
                                                   PA1  PA2  PA3
Correlation of (regression) scores with factors   0.93 0.84 0.79
Multiple R square of scores with factors          0.86 0.71 0.62
Minimum correlation of possible factor scores     0.72 0.43 0.25
  • Maximum likelihood

Maximiza la posibilidad de que los parámetros reproduzcan los datos observados

Código 
fac_ml <- data %>% select(conf_gob:conf_pres) %>% fa(nfactors = 3, fm= "ml")
fac_ml
Factor Analysis using method =  ml
Call: fa(r = ., nfactors = 3, fm = "ml")
Standardized loadings (pattern matrix) based upon correlation matrix
             ML1   ML2   ML3   h2   u2 com
conf_gob    0.77  0.13  0.02 0.72 0.28 1.1
conf_part   0.05  0.78 -0.01 0.64 0.36 1.0
conf_carab  0.51 -0.12  0.29 0.43 0.57 1.7
conf_sind  -0.19  0.24  0.46 0.27 0.73 1.9
conf_empre  0.11  0.00  0.66 0.53 0.47 1.1
conf_cong   0.14  0.44  0.30 0.52 0.48 2.0
conf_pres   0.88 -0.01 -0.03 0.75 0.25 1.0

                       ML1  ML2  ML3
SS loadings           1.83 1.02 1.00
Proportion Var        0.26 0.15 0.14
Cumulative Var        0.26 0.41 0.55
Proportion Explained  0.47 0.27 0.26
Cumulative Proportion 0.47 0.74 1.00

 With factor correlations of 
     ML1  ML2  ML3
ML1 1.00 0.48 0.52
ML2 0.48 1.00 0.45
ML3 0.52 0.45 1.00

Mean item complexity =  1.4
Test of the hypothesis that 3 factors are sufficient.

df null model =  21  with the objective function =  2.3 with Chi Square =  7858.1
df of  the model are 3  and the objective function was  0.01 

The root mean square of the residuals (RMSR) is  0.01 
The df corrected root mean square of the residuals is  0.03 

The harmonic n.obs is  3337 with the empirical chi square  14.35  with prob <  0.0025 
The total n.obs was  3417  with Likelihood Chi Square =  35.46  with prob <  0.000000097 

Tucker Lewis Index of factoring reliability =  0.971
RMSEA index =  0.056  and the 90 % confidence intervals are  0.041 0.074
BIC =  11.05
Fit based upon off diagonal values = 1
Measures of factor score adequacy             
                                                   ML1  ML2  ML3
Correlation of (regression) scores with factors   0.93 0.85 0.82
Multiple R square of scores with factors          0.86 0.73 0.67
Minimum correlation of possible factor scores     0.72 0.45 0.34

Rotación

  • Varimax (ortogonal)
Código 
fac_ml_var <- data %>% select(conf_gob:conf_pres) %>% fa(nfactors = 3, fm= "ml", rotate="varimax") # ortogonal
fac_ml_var
Factor Analysis using method =  ml
Call: fa(r = ., nfactors = 3, rotate = "varimax", fm = "ml")
Standardized loadings (pattern matrix) based upon correlation matrix
            ML1  ML2  ML3   h2   u2 com
conf_gob   0.76 0.32 0.17 0.72 0.28 1.4
conf_part  0.21 0.74 0.22 0.64 0.36 1.3
conf_carab 0.57 0.05 0.31 0.43 0.57 1.6
conf_sind  0.04 0.23 0.46 0.27 0.73 1.5
conf_empre 0.35 0.11 0.63 0.53 0.47 1.6
conf_cong  0.34 0.48 0.42 0.52 0.48 2.8
conf_pres  0.83 0.22 0.10 0.75 0.25 1.2

                       ML1  ML2  ML3
SS loadings           1.89 1.00 0.97
Proportion Var        0.27 0.14 0.14
Cumulative Var        0.27 0.41 0.55
Proportion Explained  0.49 0.26 0.25
Cumulative Proportion 0.49 0.75 1.00

Mean item complexity =  1.6
Test of the hypothesis that 3 factors are sufficient.

df null model =  21  with the objective function =  2.3 with Chi Square =  7858.1
df of  the model are 3  and the objective function was  0.01 

The root mean square of the residuals (RMSR) is  0.01 
The df corrected root mean square of the residuals is  0.03 

The harmonic n.obs is  3337 with the empirical chi square  14.35  with prob <  0.0025 
The total n.obs was  3417  with Likelihood Chi Square =  35.46  with prob <  0.000000097 

Tucker Lewis Index of factoring reliability =  0.971
RMSEA index =  0.056  and the 90 % confidence intervals are  0.041 0.074
BIC =  11.05
Fit based upon off diagonal values = 1
Measures of factor score adequacy             
                                                   ML1  ML2  ML3
Correlation of (regression) scores with factors   0.89 0.78 0.73
Multiple R square of scores with factors          0.79 0.61 0.54
Minimum correlation of possible factor scores     0.59 0.21 0.07
  • Promax (oblicua)
Código 
fac_ml_pro <- data %>% select(conf_gob:conf_pres) %>% fa(nfactors = 3, fm= "ml", rotate="promax")
fac_ml_pro
Factor Analysis using method =  ml
Call: fa(r = ., nfactors = 3, rotate = "promax", fm = "ml")
Standardized loadings (pattern matrix) based upon correlation matrix
             ML1   ML2   ML3   h2   u2 com
conf_gob    0.80  0.19 -0.09 0.72 0.28 1.1
conf_part   0.03  0.78  0.01 0.64 0.36 1.0
conf_carab  0.57 -0.14  0.23 0.43 0.57 1.4
conf_sind  -0.15  0.13  0.51 0.27 0.73 1.3
conf_empre  0.19 -0.12  0.67 0.53 0.47 1.2
conf_cong   0.17  0.39  0.30 0.52 0.48 2.3
conf_pres   0.91  0.07 -0.16 0.75 0.25 1.1

                       ML1  ML2  ML3
SS loadings           1.98 0.96 0.92
Proportion Var        0.28 0.14 0.13
Cumulative Var        0.28 0.42 0.55
Proportion Explained  0.51 0.25 0.24
Cumulative Proportion 0.51 0.76 1.00

 With factor correlations of 
     ML1  ML2  ML3
ML1 1.00 0.48 0.57
ML2 0.48 1.00 0.56
ML3 0.57 0.56 1.00

Mean item complexity =  1.4
Test of the hypothesis that 3 factors are sufficient.

df null model =  21  with the objective function =  2.3 with Chi Square =  7858.1
df of  the model are 3  and the objective function was  0.01 

The root mean square of the residuals (RMSR) is  0.01 
The df corrected root mean square of the residuals is  0.03 

The harmonic n.obs is  3337 with the empirical chi square  14.35  with prob <  0.0025 
The total n.obs was  3417  with Likelihood Chi Square =  35.46  with prob <  0.000000097 

Tucker Lewis Index of factoring reliability =  0.971
RMSEA index =  0.056  and the 90 % confidence intervals are  0.041 0.074
BIC =  11.05
Fit based upon off diagonal values = 1
Measures of factor score adequacy             
                                                   ML1  ML2  ML3
Correlation of (regression) scores with factors   0.93 0.85 0.83
Multiple R square of scores with factors          0.87 0.72 0.69
Minimum correlation of possible factor scores     0.74 0.45 0.38

Casi automático con sjPlot

Código 
data %>% select(conf_gob:conf_pres) %>% sjPlot::tab_fa(method = "ml", rotation = "promax", show.comm = TRUE, title = "Análisis factorial de confianza en instituciones")
Parallel analysis suggests that the number of factors =  3  and the number of components =  NA
Análisis factorial de confianza en instituciones
  Factor 1 Factor 2 Factor 3 Communality
Grado de confianza: El Gobierno 0.80 0.19 -0.09 0.72
Grado de confianza: Los Partidos
Politicos		 0.03 0.78 0.01 0.64
Grado de confianza: Carabineros 0.57 -0.14 0.23 0.43
Grado de confianza: Los Sindicatos -0.15 0.13 0.51 0.27
Grado de confianza: Las Empresas
Privadas		 0.19 -0.12 0.67 0.53
Grado de confianza: El Congreso Nacional 0.17 0.39 0.30 0.52
Grado de confianza: El Presidente/a de
la Republica		 0.91 0.07 -0.16 0.75
Total Communalities 3.85
Cronbach's α 0.78 0.67 0.48

Luego de realizar el Análisis factorial exploratorio existen varias alternativas sobre los pasos a seguir. Por ejemplo, es posible estimar un promedio simple entre cada una de las variables de los factores. Otra opción es estimar puntajes factoriales.

Puntajes factoriales

Código 
fac_ml <- data %>% select(conf_gob:conf_pres) %>% fa(nfactors = 3, fm= "ml", rotate = "promax", scores = "regression")
fac_ml
Factor Analysis using method =  ml
Call: fa(r = ., nfactors = 3, rotate = "promax", scores = "regression", 
    fm = "ml")
Standardized loadings (pattern matrix) based upon correlation matrix
             ML1   ML2   ML3   h2   u2 com
conf_gob    0.80  0.19 -0.09 0.72 0.28 1.1
conf_part   0.03  0.78  0.01 0.64 0.36 1.0
conf_carab  0.57 -0.14  0.23 0.43 0.57 1.4
conf_sind  -0.15  0.13  0.51 0.27 0.73 1.3
conf_empre  0.19 -0.12  0.67 0.53 0.47 1.2
conf_cong   0.17  0.39  0.30 0.52 0.48 2.3
conf_pres   0.91  0.07 -0.16 0.75 0.25 1.1

                       ML1  ML2  ML3
SS loadings           1.98 0.96 0.92
Proportion Var        0.28 0.14 0.13
Cumulative Var        0.28 0.42 0.55
Proportion Explained  0.51 0.25 0.24
Cumulative Proportion 0.51 0.76 1.00

 With factor correlations of 
     ML1  ML2  ML3
ML1 1.00 0.48 0.57
ML2 0.48 1.00 0.56
ML3 0.57 0.56 1.00

Mean item complexity =  1.4
Test of the hypothesis that 3 factors are sufficient.

df null model =  21  with the objective function =  2.3 with Chi Square =  7858.1
df of  the model are 3  and the objective function was  0.01 

The root mean square of the residuals (RMSR) is  0.01 
The df corrected root mean square of the residuals is  0.03 

The harmonic n.obs is  3337 with the empirical chi square  14.35  with prob <  0.0025 
The total n.obs was  3417  with Likelihood Chi Square =  35.46  with prob <  0.000000097 

Tucker Lewis Index of factoring reliability =  0.971
RMSEA index =  0.056  and the 90 % confidence intervals are  0.041 0.074
BIC =  11.05
Fit based upon off diagonal values = 1
Measures of factor score adequacy             
                                                   ML1  ML2  ML3
Correlation of (regression) scores with factors   0.93 0.85 0.83
Multiple R square of scores with factors          0.87 0.72 0.69
Minimum correlation of possible factor scores     0.74 0.45 0.38
Código 
data <- cbind(data, fac_ml$scores)
Código 
data %>% select(conf_inst, ML1, ML2, ML3) %>% head(10)
   conf_inst        ML1        ML2        ML3
1   1.000000 -0.8382387 -0.4724225 -0.7851196
2   1.333333 -0.5980196 -0.6372386 -0.7486267
3   1.000000 -0.8356784 -0.5480919 -0.9833033
4   2.833333  2.1363615  0.1859941  0.9509994
5   1.166667 -0.7238739 -0.5542404 -0.5297908
6   1.000000 -0.8356784 -0.5480919 -0.9833033
7   1.000000 -0.8356784 -0.5480919 -0.9833033
8   1.666667 -0.4275077  0.2577645  0.6781084
9   1.000000 -0.8356784 -0.5480919 -0.9833033
10  1.333333 -0.5980196 -0.6372386 -0.7486267

Factor 1

Código 
summary(data$ML1)
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max.     NA's 
-0.84894 -0.72453 -0.38400 -0.01872  0.50205  3.94763      222

Factor 2

Código 
summary(data$ML2)
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max.     NA's 
-0.75098 -0.54809 -0.40290 -0.00971  0.16165  5.39270      222

Factor 3

Código 
summary(data$ML3)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
-1.1852 -0.7486 -0.1423 -0.0131  0.5225  3.7504     222

Renombramos los factores para darle más sentido a la interpretación

Código 
data<- data %>% rename(inst_ejecutivo=ML1,
                inst_partidos=ML2,
                inst_trabajo=ML3)

Ahora probar cada uno de estos puntajes en un modelo de regresión

Código 
data<-na.omit(data)
reg1 <- lm(satis_dem~conf_inst, data=data)
reg2 <- lm(satis_dem~inst_ejecutivo, data=data)
reg3 <- lm(satis_dem~inst_partidos, data=data)
reg4 <- lm(satis_dem~inst_trabajo, data=data)
reg5 <- lm(satis_dem~inst_ejecutivo+inst_partidos+inst_trabajo, data=data)
Código 
texreg::knitreg(list(reg1, reg2, reg3, reg4, reg5))
Statistical models
  Model 1 Model 2 Model 3 Model 4 Model 5
(Intercept) 0.68*** 1.70*** 1.70*** 1.70*** 1.70***
  (0.04) (0.01) (0.02) (0.02) (0.01)
conf_inst 0.61***        
  (0.02)        
inst_ejecutivo   0.42***     0.34***
    (0.02)     (0.02)
inst_partidos     0.39***   0.17***
      (0.02)   (0.03)
inst_trabajo       0.37*** -0.02
        (0.02) (0.03)
R2 0.18 0.18 0.13 0.11 0.20
Adj. R2 0.18 0.18 0.13 0.11 0.20
Num. obs. 3134 3134 3134 3134 3134
***p < 0.001; **p < 0.01; *p < 0.05