ANALISIS FACTORIAL EXPLORATORIO TAREA 11
Alexandra Arroyo
2024-11-20
Ejercicio 2
Data1 <- read.csv("Calificaciones.csv")
head(Data1)## Edad Grado Naturales Sociales Matematicas Espanol Ingles Deportes Humanidades
## 1 17 11 80 75 79 69 67 93 91
## 2 13 8 78 74 98 61 57 99 97
## 3 14 9 79 83 90 61 58 99 92
## 4 15 9 90 95 88 88 85 94 94
## 5 18 12 89 85 69 78 82 95 92
## 6 11 6 89 80 95 86 85 93 90
## Etica
## 1 85
## 2 99
## 3 91
## 4 87
## 5 73
## 6 100Data solo numerica:
Data_numeric1 <- Data1[sapply(Data1, is.numeric)]
Data_numeric1## Edad Grado Naturales Sociales Matematicas Espanol Ingles Deportes
## 1 17 11 80 75 79 69 67 93
## 2 13 8 78 74 98 61 57 99
## 3 14 9 79 83 90 61 58 99
## 4 15 9 90 95 88 88 85 94
## 5 18 12 89 85 69 78 82 95
## 6 11 6 89 80 95 86 85 93
## 7 17 11 81 81 90 71 69 93
## 8 12 7 87 95 86 76 79 94
## 9 14 9 83 90 68 63 67 98
## 10 17 11 82 82 82 72 67 96
## 11 10 6 85 77 95 75 78 91
## 12 14 9 89 96 78 82 77 100
## 13 18 12 82 77 89 70 74 90
## 14 15 9 89 81 69 77 79 98
## 15 11 6 80 78 85 63 60 99
## 16 11 6 83 81 92 64 69 96
## 17 14 9 90 89 85 77 81 99
## 18 10 6 84 77 74 69 71 97
## 19 18 12 90 82 88 76 79 100
## 20 12 7 94 92 79 89 87 100
## 21 14 9 80 70 85 62 63 96
## 22 16 10 89 81 97 82 85 93
## 23 15 9 86 93 67 80 78 93
## 24 18 12 88 88 90 83 83 92
## 25 12 7 89 88 90 81 78 100
## 26 17 11 85 77 87 68 73 96
## 27 13 8 80 81 77 71 67 92
## 28 17 11 79 73 71 65 61 97
## 29 17 11 88 89 92 79 84 91
## 30 17 11 81 90 69 64 64 98
## 31 11 6 86 84 78 69 72 100
## 32 13 8 84 75 74 74 70 97
## 33 16 10 83 80 73 69 71 94
## 34 16 10 90 81 66 77 80 99
## 35 10 6 90 94 88 84 86 94
## 36 16 10 84 88 77 71 75 93
## 37 13 8 79 89 82 60 64 94
## 38 14 9 76 79 88 66 61 90
## 39 10 6 87 95 70 87 83 90
## 40 18 12 90 95 95 86 88 92
## 41 11 6 89 94 76 85 82 95
## 42 18 12 84 91 97 79 77 90
## 43 12 7 86 94 76 81 82 90
## 44 18 12 82 92 99 65 68 96
## 45 13 8 89 94 80 81 84 94
## 46 15 9 83 77 70 77 73 93
## 47 17 11 93 84 70 86 89 97
## 48 14 9 90 90 87 78 79 100
## 49 12 7 82 79 79 69 68 96
## 50 14 9 89 83 79 88 87 91
## 51 16 10 82 81 95 66 67 97
## 52 14 9 82 74 69 70 66 97
## 53 12 7 85 77 90 71 74 95
## 54 15 9 83 90 73 67 67 98
## 55 12 7 88 95 66 79 80 96
## 56 12 7 74 84 90 60 57 91
## 57 18 12 93 96 92 83 86 100
## 58 18 12 90 99 84 88 87 92
## 59 11 6 91 89 100 86 91 91
## 60 17 11 94 90 91 83 88 99
## 61 18 12 88 97 75 90 86 90
## 62 15 9 84 91 67 66 71 97
## 63 12 7 89 90 83 77 79 99
## 64 13 8 80 76 75 61 61 98
## 65 16 10 84 77 68 69 70 97
## 66 10 6 86 89 93 76 81 91
## 67 17 11 90 83 78 82 85 95
## 68 16 10 92 99 78 87 89 95
## 69 12 7 84 89 71 70 67 100
## 70 18 12 77 82 66 67 62 92
## 71 10 6 88 91 83 87 83 93
## 72 11 6 81 83 83 66 65 97
## 73 16 10 84 86 87 67 67 100
## 74 15 9 78 87 78 61 63 93
## 75 11 6 88 88 71 86 84 92
## 76 13 8 88 78 68 83 83 93
## 77 13 8 78 81 74 67 64 92
## 78 12 7 84 88 85 66 71 96
## 79 17 11 86 89 90 84 81 90
## 80 11 6 87 92 78 80 80 94
## 81 14 9 83 83 86 72 74 91
## 82 16 10 86 85 82 79 79 93
## 83 17 11 92 96 89 85 88 95
## 84 17 11 95 91 80 89 90 100
## 85 14 9 77 86 86 62 61 92
## 86 16 10 83 76 88 63 67 99
## 87 16 10 91 89 83 88 89 92
## 88 16 10 77 74 76 62 59 94
## 89 11 6 80 83 91 61 65 95
## 90 16 10 88 92 81 75 80 96
## 91 15 9 85 84 79 79 79 91
## 92 18 12 82 77 68 71 68 96
## 93 12 7 92 90 72 83 83 100
## 94 15 9 90 80 79 81 86 94
## 95 12 7 81 83 87 67 72 90
## 96 17 11 90 98 75 89 85 95
## 97 17 11 77 79 98 63 62 92
## 98 14 9 88 86 74 81 85 90
## 99 15 9 93 97 81 83 87 98
## 100 17 11 77 83 98 63 62 92
## Humanidades Etica
## 1 91 85
## 2 97 99
## 3 92 91
## 4 94 87
## 5 92 73
## 6 90 100
## 7 86 91
## 8 94 93
## 9 96 70
## 10 88 84
## 11 82 96
## 12 93 76
## 13 84 87
## 14 98 71
## 15 96 84
## 16 95 92
## 17 97 93
## 18 97 74
## 19 98 88
## 20 98 80
## 21 86 89
## 22 84 96
## 23 83 74
## 24 83 89
## 25 95 90
## 26 88 90
## 27 86 83
## 28 93 73
## 29 84 94
## 30 92 76
## 31 91 80
## 32 94 72
## 33 92 77
## 34 98 72
## 35 85 94
## 36 92 75
## 37 93 84
## 38 83 88
## 39 85 73
## 40 83 97
## 41 86 78
## 42 86 99
## 43 90 75
## 44 95 100
## 45 84 84
## 46 90 72
## 47 94 70
## 48 97 88
## 49 92 82
## 50 87 79
## 51 87 100
## 52 92 74
## 53 95 97
## 54 93 77
## 55 87 72
## 56 81 97
## 57 95 93
## 58 91 84
## 59 85 100
## 60 93 94
## 61 90 73
## 62 93 71
## 63 91 86
## 64 95 75
## 65 92 75
## 66 90 98
## 67 86 77
## 68 86 78
## 69 94 75
## 70 84 70
## 71 86 81
## 72 92 86
## 73 94 87
## 74 83 77
## 75 86 76
## 76 89 70
## 77 88 75
## 78 96 90
## 79 82 95
## 80 86 77
## 81 86 89
## 82 83 83
## 83 90 89
## 84 97 86
## 85 90 91
## 86 98 91
## 87 82 85
## 88 84 84
## 89 87 96
## 90 87 80
## 91 91 86
## 92 96 72
## 93 95 74
## 94 90 80
## 95 88 91
## 96 91 77
## 97 84 97
## 98 88 77
## 99 97 80
## 100 84 97Estadisticas descriptivas:
Data_numeric1 <- Data1[sapply(Data1, is.numeric)]
col_means1 <- colMeans(Data_numeric1)
Medias1 <- apply(Data_numeric1[,],2,mean)
Des_st1 <- apply(Data_numeric1[,],2,sd)
Coef_Var1 <- Des_st1/Medias1
Descriptivas1 <-rbind(Medias1,Des_st1,Coef_Var1)
round(Descriptivas1,2)## Edad Grado Naturales Sociales Matematicas Espanol Ingles Deportes
## Medias1 14.44 8.99 85.30 85.61 81.62 74.75 75.22 94.92
## Des_st1 2.51 1.98 4.81 6.99 9.24 9.00 9.47 3.19
## Coef_Var1 0.17 0.22 0.06 0.08 0.11 0.12 0.13 0.03
## Humanidades Etica
## Medias1 89.99 83.92
## Des_st1 4.82 9.08
## Coef_Var1 0.05 0.11El análisis exploratorio descriptivo muestra que la edad media de los estudiantes es 14.44 años (CV=0.17), y se encuentran principalmente en el grado noveno (9) (media=8.99, CV=0.22). Las calificaciones en asignaturas como Deportes (media=94.92, CV=0.03) y Humanidades (media=89.99, CV=0.05) tienen alta consistencia, mientras que asignaturas como Español (media=74.75, CV=0.12) e Inglés (media=75.22, CV=0.13) muestran mayor variabilidad. En general, las clases presentan buenas calificaciones promedio, con una menor variabilidad en los cursis prácticos como Deportes y una dispersión moderada en las teóricas como Matemáticas y Ética.
Aplicacion de Analisis Factorial Exploratorio (EFA) con enfoque en las calificaciones de los diferentes cursos
Data_C <- Data1[, c("Naturales", "Sociales", "Espanol", "Ingles", "Deportes", "Humanidades", "Etica")]
Data_C## Naturales Sociales Espanol Ingles Deportes Humanidades Etica
## 1 80 75 69 67 93 91 85
## 2 78 74 61 57 99 97 99
## 3 79 83 61 58 99 92 91
## 4 90 95 88 85 94 94 87
## 5 89 85 78 82 95 92 73
## 6 89 80 86 85 93 90 100
## 7 81 81 71 69 93 86 91
## 8 87 95 76 79 94 94 93
## 9 83 90 63 67 98 96 70
## 10 82 82 72 67 96 88 84
## 11 85 77 75 78 91 82 96
## 12 89 96 82 77 100 93 76
## 13 82 77 70 74 90 84 87
## 14 89 81 77 79 98 98 71
## 15 80 78 63 60 99 96 84
## 16 83 81 64 69 96 95 92
## 17 90 89 77 81 99 97 93
## 18 84 77 69 71 97 97 74
## 19 90 82 76 79 100 98 88
## 20 94 92 89 87 100 98 80
## 21 80 70 62 63 96 86 89
## 22 89 81 82 85 93 84 96
## 23 86 93 80 78 93 83 74
## 24 88 88 83 83 92 83 89
## 25 89 88 81 78 100 95 90
## 26 85 77 68 73 96 88 90
## 27 80 81 71 67 92 86 83
## 28 79 73 65 61 97 93 73
## 29 88 89 79 84 91 84 94
## 30 81 90 64 64 98 92 76
## 31 86 84 69 72 100 91 80
## 32 84 75 74 70 97 94 72
## 33 83 80 69 71 94 92 77
## 34 90 81 77 80 99 98 72
## 35 90 94 84 86 94 85 94
## 36 84 88 71 75 93 92 75
## 37 79 89 60 64 94 93 84
## 38 76 79 66 61 90 83 88
## 39 87 95 87 83 90 85 73
## 40 90 95 86 88 92 83 97
## 41 89 94 85 82 95 86 78
## 42 84 91 79 77 90 86 99
## 43 86 94 81 82 90 90 75
## 44 82 92 65 68 96 95 100
## 45 89 94 81 84 94 84 84
## 46 83 77 77 73 93 90 72
## 47 93 84 86 89 97 94 70
## 48 90 90 78 79 100 97 88
## 49 82 79 69 68 96 92 82
## 50 89 83 88 87 91 87 79
## 51 82 81 66 67 97 87 100
## 52 82 74 70 66 97 92 74
## 53 85 77 71 74 95 95 97
## 54 83 90 67 67 98 93 77
## 55 88 95 79 80 96 87 72
## 56 74 84 60 57 91 81 97
## 57 93 96 83 86 100 95 93
## 58 90 99 88 87 92 91 84
## 59 91 89 86 91 91 85 100
## 60 94 90 83 88 99 93 94
## 61 88 97 90 86 90 90 73
## 62 84 91 66 71 97 93 71
## 63 89 90 77 79 99 91 86
## 64 80 76 61 61 98 95 75
## 65 84 77 69 70 97 92 75
## 66 86 89 76 81 91 90 98
## 67 90 83 82 85 95 86 77
## 68 92 99 87 89 95 86 78
## 69 84 89 70 67 100 94 75
## 70 77 82 67 62 92 84 70
## 71 88 91 87 83 93 86 81
## 72 81 83 66 65 97 92 86
## 73 84 86 67 67 100 94 87
## 74 78 87 61 63 93 83 77
## 75 88 88 86 84 92 86 76
## 76 88 78 83 83 93 89 70
## 77 78 81 67 64 92 88 75
## 78 84 88 66 71 96 96 90
## 79 86 89 84 81 90 82 95
## 80 87 92 80 80 94 86 77
## 81 83 83 72 74 91 86 89
## 82 86 85 79 79 93 83 83
## 83 92 96 85 88 95 90 89
## 84 95 91 89 90 100 97 86
## 85 77 86 62 61 92 90 91
## 86 83 76 63 67 99 98 91
## 87 91 89 88 89 92 82 85
## 88 77 74 62 59 94 84 84
## 89 80 83 61 65 95 87 96
## 90 88 92 75 80 96 87 80
## 91 85 84 79 79 91 91 86
## 92 82 77 71 68 96 96 72
## 93 92 90 83 83 100 95 74
## 94 90 80 81 86 94 90 80
## 95 81 83 67 72 90 88 91
## 96 90 98 89 85 95 91 77
## 97 77 79 63 62 92 84 97
## 98 88 86 81 85 90 88 77
## 99 93 97 83 87 98 97 80
## 100 77 83 63 62 92 84 97Paso 1: Verificar que la matiz de datos sea factorizable
Matriz de Correlacion
library(polycor)## Warning: package 'polycor' was built under R version 4.3.3R1 <- hetcor(Data_C)$correlations
R1## Naturales Sociales Espanol Ingles Deportes
## Naturales 1.00000000 0.56828476 0.8763763 0.94035307 0.21363165
## Sociales 0.56828476 1.00000000 0.5780291 0.58684997 -0.02769219
## Espanol 0.87637631 0.57802908 1.0000000 0.94410134 -0.15860407
## Ingles 0.94035307 0.58684997 0.9441013 1.00000000 -0.12750230
## Deportes 0.21363165 -0.02769219 -0.1586041 -0.12750230 1.00000000
## Humanidades 0.19550879 -0.04272344 -0.1095165 -0.05997206 0.74346406
## Etica -0.09477832 -0.02803799 -0.1177592 -0.03998243 -0.16102119
## Humanidades Etica
## Naturales 0.19550879 -0.09477832
## Sociales -0.04272344 -0.02803799
## Espanol -0.10951646 -0.11775924
## Ingles -0.05997206 -0.03998243
## Deportes 0.74346406 -0.16102119
## Humanidades 1.00000000 -0.19982447
## Etica -0.19982447 1.00000000library(ggcorrplot)## Warning: package 'ggcorrplot' was built under R version 4.3.3## Loading required package: ggplot2## Warning: package 'ggplot2' was built under R version 4.3.3ggcorrplot(R1,type="lower",hc.order = T)
En la grafica podemos observar una excelente Correlacion entre las Variables Naturales + Ingles, Espanol + Ingles, Espanol + Naturales y Deportes + Humanidades. Sin embargo, predonimam mas las que tienen poca correlacion o hasta nada de correlacion como por ejemplo Etica + Ingles.
Prueba de esfericidad de Bartlett:
library(psych)## Warning: package 'psych' was built under R version 4.3.3##
## Attaching package: 'psych'## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha## The following object is masked from 'package:polycor':
##
## polyserialcortest.bartlett(Data_C)$p.value## R was not square, finding R from data## [1] 5.959529e-181Dado que el p-value = 0 , rechazamos la hipotesis nula y concluimos que las variables efectivamente estan correlacionadas entre si.Sin embargo ralizamos otra prueba para confirmar.
Prueba de KMO
KMO(R1)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = R1)
## Overall MSA = 0.59
## MSA for each item =
## Naturales Sociales Espanol Ingles Deportes Humanidades
## 0.52 0.99 0.94 0.53 0.26 0.91
## Etica
## 0.46Un valor global de 0.59 nos afirma que estas variables son Malas para aplicar un EFA, el MSA nos indica que casi ninguna de las variables son importantes para el analisis.LO ideal seria eliminar variables con baja adecuacion para mejorar la matriz de correlacion.
Paso 2: Elegir un método y extraer los factores:
Metodos utilizados: ejes principales y minimo residuo
Prueba de dos modelos con cinco factores:
library(psych)
m1_C <- fa(R1, nfactors = 5, rotate = "none",
fm="paf") # modelo de ejes principales## factor method not specified correctly, minimum residual (unweighted least squares usedm1_C## Factor Analysis using method = minres
## Call: fa(r = R1, nfactors = 5, rotate = "none", fm = "paf")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 MR3 MR4 MR5 h2 u2 com
## Naturales 0.96 0.25 0.10 -0.06 0.00 1.00 0.0029 1.2
## Sociales 0.60 -0.03 0.06 0.08 -0.08 0.37 0.6266 1.1
## Espanol 0.97 -0.12 -0.16 0.11 0.06 0.99 0.0051 1.1
## Ingles 0.99 -0.08 0.06 -0.11 -0.01 1.00 0.0034 1.0
## Deportes -0.04 0.98 0.12 0.15 0.01 1.00 0.0048 1.1
## Humanidades -0.01 0.80 -0.09 -0.17 0.01 0.67 0.3295 1.1
## Etica -0.09 -0.21 0.39 -0.02 0.04 0.21 0.7911 1.7
##
## MR1 MR2 MR3 MR4 MR5
## SS loadings 3.20 1.72 0.22 0.09 0.01
## Proportion Var 0.46 0.25 0.03 0.01 0.00
## Cumulative Var 0.46 0.70 0.73 0.75 0.75
## Proportion Explained 0.61 0.33 0.04 0.02 0.00
## Cumulative Proportion 0.61 0.94 0.98 1.00 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 5 factors are sufficient.
##
## df null model = 21 with the objective function = 9.59
## df of the model are -4 and the objective function was 0.34
##
## The root mean square of the residuals (RMSR) is 0
## The df corrected root mean square of the residuals is NA
##
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR2 MR3 MR4 MR5
## Correlation of (regression) scores with factors 1 0.99 0.78 0.80 0.25
## Multiple R square of scores with factors 1 0.97 0.60 0.63 0.06
## Minimum correlation of possible factor scores 1 0.94 0.20 0.27 -0.87m2_C <- fa(R1, nfactors = 5, rotate = "none",
fm="minres") # minimo residuo
m2_C## Factor Analysis using method = minres
## Call: fa(r = R1, nfactors = 5, rotate = "none", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 MR3 MR4 MR5 h2 u2 com
## Naturales 0.96 0.25 0.10 -0.06 0.00 1.00 0.0029 1.2
## Sociales 0.60 -0.03 0.06 0.08 -0.08 0.37 0.6266 1.1
## Espanol 0.97 -0.12 -0.16 0.11 0.06 0.99 0.0051 1.1
## Ingles 0.99 -0.08 0.06 -0.11 -0.01 1.00 0.0034 1.0
## Deportes -0.04 0.98 0.12 0.15 0.01 1.00 0.0048 1.1
## Humanidades -0.01 0.80 -0.09 -0.17 0.01 0.67 0.3295 1.1
## Etica -0.09 -0.21 0.39 -0.02 0.04 0.21 0.7911 1.7
##
## MR1 MR2 MR3 MR4 MR5
## SS loadings 3.20 1.72 0.22 0.09 0.01
## Proportion Var 0.46 0.25 0.03 0.01 0.00
## Cumulative Var 0.46 0.70 0.73 0.75 0.75
## Proportion Explained 0.61 0.33 0.04 0.02 0.00
## Cumulative Proportion 0.61 0.94 0.98 1.00 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 5 factors are sufficient.
##
## df null model = 21 with the objective function = 9.59
## df of the model are -4 and the objective function was 0.34
##
## The root mean square of the residuals (RMSR) is 0
## The df corrected root mean square of the residuals is NA
##
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR2 MR3 MR4 MR5
## Correlation of (regression) scores with factors 1 0.99 0.78 0.80 0.25
## Multiple R square of scores with factors 1 0.97 0.60 0.63 0.06
## Minimum correlation of possible factor scores 1 0.94 0.20 0.27 -0.87Comparación de las comunalidades:
c1_C <- sort(m1_C$communality,decreasing = T)
c1_C## Naturales Ingles Deportes Espanol Humanidades Sociales
## 0.9970588 0.9965597 0.9951524 0.9949174 0.6704766 0.3733881
## Etica
## 0.2089319c2_C <- sort(m2_C$communality,decreasing = T)
c2_C## Naturales Ingles Deportes Espanol Humanidades Sociales
## 0.9970588 0.9965597 0.9951524 0.9949174 0.6704766 0.3733881
## Etica
## 0.2089319head(cbind(c1_C,c2_C))## c1_C c2_C
## Naturales 0.9970588 0.9970588
## Ingles 0.9965597 0.9965597
## Deportes 0.9951524 0.9951524
## Espanol 0.9949174 0.9949174
## Humanidades 0.6704766 0.6704766
## Sociales 0.3733881 0.3733881Comparación de las unicidades:
u1_C <- sort(m1_C$uniquenesses,decreasing = T)
u2_C <- sort(m2_C$uniquenesses,decreasing = T)
head(cbind(u1_C,u2_C))## u1_C u2_C
## Etica 0.791068139 0.791068139
## Sociales 0.626611934 0.626611934
## Humanidades 0.329523358 0.329523358
## Espanol 0.005082593 0.005082593
## Deportes 0.004847646 0.004847646
## Ingles 0.003440298 0.003440298Las asignaturas de ciencias naturales, inglés, deportes y español están bien representadas por los factores extraídos, con bajas unicidades y altas comunalidades, lo que indica que la mayoría de su varianza es explicada por estos factores. En cambio, humanidades y ciencias sociales tienen una mayor parte de su varianza no explicada, sugiriendo la influencia de otros factores no capturados en el análisis. Ética, con baja comunalidad y alta unicidad, muestra una relación débil con los factores extraídos, lo que sugiere que su desempeño depende de factores no incluidos en el modelo.
Paso 3: Determinar el número adecuado de factores:
Valores propios:
ei1 <- eigen(R1)
plot(ei1$values,type="b",pch=20,col="blue")
abline(h=1,lty=3,col="red")
ei1## eigen() decomposition
## $values
## [1] 3.289950285 1.895480039 0.928723827 0.560099315 0.260332890 0.064144794
## [7] 0.001268849
##
## $vectors
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -0.521219766 0.16741708 0.10310189 -0.22257636 -0.15526218 -0.36582447
## [2,] -0.400483472 -0.03139281 0.08050003 0.90923263 0.07360354 -0.00507103
## [3,] -0.526076777 -0.08387257 -0.07686688 -0.22469997 0.01757025 0.81208927
## [4,] -0.535775617 -0.06048240 0.03243915 -0.24832590 0.06411951 -0.42329474
## [5,] 0.019163911 0.66591091 0.21083545 0.06696405 -0.65961156 0.13293672
## [6,] 0.003037965 0.66576697 0.14885391 -0.04742999 0.72745931 0.05594038
## [7,] 0.061271306 -0.27131215 0.95358264 -0.06975795 0.04209144 0.08171791
## [,7]
## [1,] 6.944043e-01
## [2,] 2.340358e-04
## [3,] -3.510301e-03
## [4,] -6.806457e-01
## [5,] -2.334525e-01
## [6,] -3.412923e-03
## [7,] -7.908576e-05Scree plot:
Screeplot <- scree(R1)## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
Paralelo:
Paralelo <- fa.parallel(R1, n.obs = 100, main = "Prueba de Paralelo - EFA",
ylab = "Valor Eigen")## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Parallel analysis suggests that the number of factors = 2 and the number of components = 2Paralelo## Call: fa.parallel(x = R1, n.obs = 100, main = "Prueba de Paralelo - EFA",
## ylabel = "Valor Eigen")
## Parallel analysis suggests that the number of factors = 2 and the number of components = 2
##
## Eigen Values of
##
## eigen values of factors
## [1] 3.13 0.96 0.05 0.01 -0.07 -0.21 -0.75
##
## eigen values of simulated factors
## [1] 0.82 0.28 0.13 0.04 -0.05 -0.15 -0.26
##
## eigen values of components
## [1] 3.29 1.90 0.93 0.56 0.26 0.06 0.00
##
## eigen values of simulated components
## [1] 1.41 1.24 1.09 0.99 0.86 0.77 0.65Parallel analysis suggests that the number of factors = 2 and the number of components = 2 Las otras variables tienen bajas cargas factoriales por lo que no contribuyen al modelo.
Paso 4: Rotación de los factores
library(psych)
library(GPArotation)## Warning: package 'GPArotation' was built under R version 4.3.3##
## Attaching package: 'GPArotation'## The following objects are masked from 'package:psych':
##
## equamax, varimin# Definir los tipos de rotación
rot1 <- c("none", "varimax", "quartimax", "promax")
# Función para generar el biplot con diferentes rotaciones
bi_mod1 <- function(tipo) {biplot.psych(fa(Data_C, nfactors = 2, fm = "pa", rotate = tipo), main = paste("Biplot con rotación", tipo), col = c("red", "black"),pch = c(5, 19))}Aplicar la función a cada tipo de rotación
sapply(rot1, bi_mod1)## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## $none
## NULL
##
## $varimax
## NULL
##
## $quartimax
## NULL
##
## $promax
## NULLComo la rotacion Varimax maximiza la varianza de las cargas factoriales dentro de cada factor, utilizare esta rotacion pues facilita la interpretacion con una estructura clara.
Paso 5: Interpretación de resultados:
modelo_varimax1 <- fa(R1,nfactors = 2,rotate = "varimax",fa="ml")## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.fa.diagram(modelo_varimax1)
El análisis factorial sugiere la existencia de dos factores principales. El Factor 1 (MR1) agrupa las asignaturas de Inglés, Español y Ciencias Naturales, con cargas factoriales altas (alrededor de 0.9), indicando que estas variables están relacionadas con competencias académicas generales, especialmente en el área de idiomas y ciencias. Por otro lado, el Factor 2 (MR2) incluye las asignaturas de Ciencias Sociales, Deportes, Humanidades y Ética, sin embargo solo Deportes y Humanidades también tienen cargas factoriales significativas (cercanas a 0.8 o superiores), lo que sugiere una dimensión vinculada al desarrollo social, fisico y personal. Al parecer el curso de Etica no aporta en nada al factor En conjunto, los resultados reflejan dos dimensiones latentes que resumen el desempeño académico de los estudiantes: una orientada al ámbito académico, teorico-científico y otra al desarrollo social y personal.