Ecuaciones Estructurales
Diego Campos Patiño
27-01-2021
Ecuaciones Estructurales (Análisis y Resultados)
En R existen diversos paquetes para análisis de ecuaciones estructurales. Los más conocidos son “SEM” (Fox 2006, 2010), “OpenMx” (Bates, Mehta y Fox, 2011) y “lavaan” (Rosseel 2011, 2012a, 2012b). Aunque aún está en fase de desarrollo, “lavaan” permite escribir los modelos de medida y estructurales más sencillamente que los otros dos paquetes, y permite realizar análisis relativamente complejos, como el análisis de grupos de ecuaciones estructurales, o el uso de métodos de estimación alternativos al de máxima verosimilitud. En este documento se utilizará un modelo de análisis factorial confirmatorio obtenido a partir de nueve de las 26 variables de HolzingerSwineford1939, un conjunto de datos disponible en R y que se usa frecuentemente en documentos sobre ecuaciones estructurales.
library("MBESS")
library("lavaan")## This is lavaan 0.6-7## lavaan is BETA software! Please report any bugs.##
## Attaching package: 'lavaan'## The following object is masked from 'package:MBESS':
##
## cor2covdata('HS')
hs2<-HS
hs3<-hs2[1:40,1:24]
hs3## id sex grade age month_since_birthday age_months age_years school
## 1 1 Male 7 13 1 157 13.0833 Pasteur
## 2 2 Female 7 13 7 163 13.5833 Pasteur
## 3 3 Female 7 13 1 157 13.0833 Pasteur
## 4 4 Male 7 13 2 158 13.1667 Pasteur
## 5 5 Female 7 12 2 146 12.1667 Pasteur
## 6 6 Female 7 14 1 169 14.0833 Pasteur
## 7 7 Male 7 12 1 145 12.0833 Pasteur
## 8 8 Female 7 12 2 146 12.1667 Pasteur
## 9 9 Female 7 13 0 156 13.0000 Pasteur
## 10 11 Female 7 12 5 149 12.4167 Pasteur
## 11 12 Male 7 12 2 146 12.1667 Pasteur
## 12 13 Male 7 12 11 155 12.9167 Pasteur
## 13 14 Female 7 12 7 151 12.5833 Pasteur
## 14 15 Female 7 12 8 152 12.6667 Pasteur
## 15 16 Male 7 12 6 150 12.5000 Pasteur
## 16 17 Female 7 12 1 145 12.0833 Pasteur
## 17 18 Female 7 14 11 179 14.9167 Pasteur
## 18 19 Male 7 13 5 161 13.4167 Pasteur
## 19 20 Female 7 12 8 152 12.6667 Pasteur
## 20 21 Female 7 12 3 147 12.2500 Pasteur
## 21 22 Male 7 14 10 178 14.8333 Pasteur
## 22 23 Male 7 12 9 153 12.7500 Pasteur
## 23 24 Male 7 12 11 155 12.9167 Pasteur
## 24 25 Female 7 12 8 152 12.6667 Pasteur
## 25 26 Male 7 12 3 147 12.2500 Pasteur
## 26 27 Male 7 12 7 151 12.5833 Pasteur
## 27 28 Male 7 12 8 152 12.6667 Pasteur
## 28 29 Female 7 13 2 158 13.1667 Pasteur
## 29 30 Female 7 12 5 149 12.4167 Pasteur
## 30 31 Female 7 12 2 146 12.1667 Pasteur
## 31 33 Female 7 12 7 151 12.5833 Pasteur
## 32 34 Male 7 16 0 192 16.0000 Pasteur
## 33 35 Female 7 12 2 146 12.1667 Pasteur
## 34 36 Female 7 12 3 147 12.2500 Pasteur
## 35 38 Female 7 13 3 159 13.2500 Pasteur
## 36 39 Male 7 13 10 166 13.8333 Pasteur
## 37 40 Male 7 12 9 153 12.7500 Pasteur
## 38 41 Female 7 12 8 152 12.6667 Pasteur
## 39 42 Female 7 12 6 150 12.5000 Pasteur
## 40 43 Male 7 12 5 149 12.4167 Pasteur
## t1_visual_perception t2_cubes t3_paper_form_board t4_lozenges
## 1 20 31 12 3
## 2 32 21 12 17
## 3 27 21 12 15
## 4 32 31 16 24
## 5 29 19 12 7
## 6 32 20 11 18
## 7 17 24 12 8
## 8 34 25 13 15
## 9 27 23 11 12
## 10 21 21 10 6
## 11 22 23 13 16
## 12 35 24 15 23
## 13 34 18 15 33
## 14 36 22 16 14
## 15 35 23 13 29
## 16 28 19 13 19
## 17 26 19 18 12
## 18 30 27 17 18
## 19 34 21 14 32
## 20 38 35 13 24
## 21 35 32 17 16
## 22 40 34 16 33
## 23 30 25 16 15
## 24 23 22 15 13
## 25 34 22 12 10
## 26 32 16 16 27
## 27 33 21 16 36
## 28 36 20 18 17
## 29 28 24 14 34
## 30 30 18 13 6
## 31 21 23 14 11
## 32 18 24 17 2
## 33 30 21 12 14
## 34 25 24 12 19
## 35 20 15 13 12
## 36 29 21 14 4
## 37 33 28 15 28
## 38 23 18 12 18
## 39 38 16 9 31
## 40 35 31 19 20
## t5_general_information t6_paragraph_comprehension t7_sentence
## 1 40 7 23
## 2 34 5 12
## 3 20 3 7
## 4 42 8 18
## 5 37 8 16
## 6 31 3 12
## 7 40 10 24
## 8 29 11 17
## 9 29 8 23
## 10 33 8 20
## 11 38 6 14
## 12 33 8 18
## 13 33 8 16
## 14 32 14 16
## 15 54 15 22
## 16 27 8 17
## 17 35 6 16
## 18 25 6 10
## 19 62 13 21
## 20 41 11 15
## 21 22 5 10
## 22 24 6 13
## 23 37 10 23
## 24 35 8 12
## 25 45 7 15
## 26 46 5 14
## 27 18 8 9
## 28 27 5 12
## 29 31 6 12
## 30 30 8 13
## 31 29 6 14
## 32 29 5 12
## 33 52 8 21
## 34 44 10 17
## 35 30 4 12
## 36 32 5 19
## 37 34 8 16
## 38 35 9 12
## 39 47 12 21
## 40 58 9 21
## t8_word_classification t9_word_meaning t10_addition t11_code
## 1 22 9 78 74
## 2 22 9 87 84
## 3 12 3 75 49
## 4 21 17 69 65
## 5 25 18 85 63
## 6 25 6 100 92
## 7 32 20 108 65
## 8 25 9 78 80
## 9 19 19 104 52
## 10 25 18 95 74
## 11 22 11 86 60
## 12 27 19 85 71
## 13 31 16 135 68
## 14 25 11 118 68
## 15 27 21 92 64
## 16 18 5 94 59
## 17 24 9 85 58
## 18 17 12 92 61
## 19 34 26 90 94
## 20 24 18 80 62
## 21 20 4 60 44
## 22 18 15 103 73
## 23 25 22 80 62
## 24 22 7 134 64
## 25 27 9 108 60
## 26 26 10 132 67
## 27 20 5 95 67
## 28 22 8 65 56
## 29 21 14 118 90
## 30 18 13 107 65
## 31 23 13 111 60
## 32 18 7 47 31
## 33 32 14 62 64
## 34 25 13 124 86
## 35 16 6 64 64
## 36 23 10 72 42
## 37 25 14 88 65
## 38 24 12 94 50
## 39 31 23 127 83
## 40 28 22 74 69
## t12_counting_groups_of_dots t13_straight_and_curved_capitals
## 1 115 229
## 2 125 285
## 3 78 159
## 4 106 175
## 5 126 213
## 6 133 270
## 7 124 175
## 8 103 132
## 9 93 265
## 10 91 157
## 11 114 155
## 12 103 149
## 13 104 211
## 14 94 160
## 15 87 211
## 16 76 185
## 17 133 189
## 18 105 196
## 19 97 207
## 20 107 177
## 21 92 194
## 22 109 252
## 23 92 180
## 24 106 244
## 25 92 149
## 26 125 156
## 27 102 163
## 28 111 159
## 29 117 310
## 30 97 196
## 31 139 215
## 32 73 121
## 33 86 173
## 34 87 203
## 35 104 174
## 36 75 177
## 37 80 191
## 38 70 183
## 39 109 184
## 40 90 176
## t14_word_recognition t15_number_recognition t16_figure_recognition
## 1 170 86 96
## 2 184 85 100
## 3 170 85 95
## 4 181 80 91
## 5 187 99 104
## 6 164 84 104
## 7 121 71 78
## 8 184 95 106
## 9 184 91 105
## 10 175 92 100
## 11 173 86 107
## 12 167 103 108
## 13 166 92 103
## 14 186 86 102
## 15 168 84 102
## 16 181 79 99
## 17 164 84 100
## 18 149 88 98
## 19 171 74 107
## 20 186 99 105
## 21 169 96 96
## 22 169 94 105
## 23 166 83 101
## 24 173 96 99
## 25 154 92 106
## 26 175 103 110
## 27 190 97 106
## 28 172 97 98
## 29 196 94 101
## 30 192 83 109
## 31 163 88 101
## 32 159 84 92
## 33 173 95 101
## 34 182 92 96
## 35 181 90 87
## 36 176 87 87
## 37 173 78 89
## 38 154 96 87
## 39 173 96 105
## 40 172 79 105Valores Faltantes por columna
## id sex
## 0 0
## grade age
## 0 0
## month_since_birthday age_months
## 0 0
## age_years school
## 0 0
## t1_visual_perception t2_cubes
## 0 0
## t3_paper_form_board t4_lozenges
## 0 0
## t5_general_information t6_paragraph_comprehension
## 0 0
## t7_sentence t8_word_classification
## 0 0
## t9_word_meaning t10_addition
## 0 0
## t11_code t12_counting_groups_of_dots
## 0 0
## t13_straight_and_curved_capitals t14_word_recognition
## 0 0
## t15_number_recognition t16_figure_recognition
## 0 0Ejemplo Ecuaciones Estructurales
Modelo <- ’ visual =~ t1_visual_perception + t2_cubes + t3_paper_form_board textual =~ t4_lozenges +t5_general_information + t6_paragraph_comprehension speed =~ t11_code + t12_counting_groups_of_dots + t13_straight_and_curved_capitals’
Las variables t1, t2 y t3 miden el factor representado por la variable latente visual. Las variables t4, t5 y t6 miden el factor textual. Las variables t11, t12 y t13 miden el factor speed.
## Warning in lav_object_post_check(object): lavaan WARNING: some estimated ov
## variances are negative## lavaan 0.6-7 ended normally after 156 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 13
##
## Number of observations 40
##
## Model Test User Model:
##
## Test statistic 18.294
## Degrees of freedom 8
## P-value (Chi-square) 0.019## lavaan 0.6-7 ended normally after 156 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 13
##
## Number of observations 40
##
## Model Test User Model:
##
## Test statistic 18.294
## Degrees of freedom 8
## P-value (Chi-square) 0.019
##
## Model Test Baseline Model:
##
## Test statistic 47.675
## Degrees of freedom 15
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.685
## Tucker-Lewis Index (TLI) 0.409
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -712.925
## Loglikelihood unrestricted model (H1) -703.777
##
## Akaike (AIC) 1451.849
## Bayesian (BIC) 1473.805
## Sample-size adjusted Bayesian (BIC) 1433.124
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.179
## 90 Percent confidence interval - lower 0.069
## 90 Percent confidence interval - upper 0.289
## P-value RMSEA <= 0.05 0.034
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.130
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## visual =~
## t1_visl_prcptn 1.000
## t2_cubes 0.173 0.162 1.071 0.284
## t3_ppr_frm_brd 0.088 0.079 1.103 0.270
## textual =~
## t4_lozenges 1.000
## t5_gnrl_nfrmtn 0.346 0.259 1.337 0.181
## t6_prgrph_cmpr 0.157 0.076 2.072 0.038
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## visual ~~
## textual 32.310 9.899 3.264 0.001
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .t1_visl_prcptn -2.004 22.584 -0.089 0.929
## .t2_cubes 22.042 4.968 4.437 0.000
## .t3_ppr_frm_brd 5.064 1.144 4.427 0.000
## .t4_lozenges 34.123 19.729 1.730 0.084
## .t5_gnrl_nfrmtn 88.863 20.275 4.383 0.000
## .t6_prgrph_cmpr 6.347 1.508 4.210 0.000
## visual 36.901 23.886 1.545 0.122
## textual 48.351 24.757 1.953 0.051## lhs op rhs est se
## 1 visual =~ t1_visual_perception 1.000 0.000
## 2 visual =~ t2_cubes 0.173 0.162
## 3 visual =~ t3_paper_form_board 0.088 0.079
## 4 textual =~ t4_lozenges 1.000 0.000
## 5 textual =~ t5_general_information 0.346 0.259
## 6 textual =~ t6_paragraph_comprehension 0.157 0.076
## 7 t1_visual_perception ~~ t1_visual_perception -2.004 22.584
## 8 t2_cubes ~~ t2_cubes 22.042 4.968
## 9 t3_paper_form_board ~~ t3_paper_form_board 5.064 1.144
## 10 t4_lozenges ~~ t4_lozenges 34.123 19.729
## 11 t5_general_information ~~ t5_general_information 88.863 20.275
## 12 t6_paragraph_comprehension ~~ t6_paragraph_comprehension 6.347 1.508
## 13 visual ~~ visual 36.901 23.886
## 14 textual ~~ textual 48.351 24.757
## 15 visual ~~ textual 32.310 9.899
## z pvalue ci.lower ci.upper
## 1 NA NA 1.000 1.000
## 2 1.071 0.284 -0.143 0.490
## 3 1.103 0.270 -0.068 0.243
## 4 NA NA 1.000 1.000
## 5 1.337 0.181 -0.161 0.853
## 6 2.072 0.038 0.009 0.305
## 7 -0.089 0.929 -46.268 42.260
## 8 4.437 0.000 12.305 31.780
## 9 4.427 0.000 2.822 7.306
## 10 1.730 0.084 -4.545 72.792
## 11 4.383 0.000 49.124 128.601
## 12 4.210 0.000 3.392 9.302
## 13 1.545 0.122 -9.914 83.716
## 14 1.953 0.051 -0.171 96.873
## 15 3.264 0.001 12.908 51.712
Bondad de ajuste
Graficas
