Testes de Colinearidade
VIF, SMA, KMO e Bartlett
Victor Ivamoto
2020/09/20
Preparação dos dados
Carrega as bibliotecas.
library(tidyverse, readxl)## -- Attaching packages -------------------------------------------- tidyverse 1.3.0 --## v ggplot2 3.3.2 v purrr 0.3.4
## v tibble 3.0.3 v dplyr 1.0.2
## v tidyr 1.1.2 v stringr 1.4.0
## v readr 1.3.1 v forcats 0.5.0## -- Conflicts ----------------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(faraway)
library(mctest, REdaS)
library(psych, corrgram)##
## Attaching package: 'psych'## The following object is masked from 'package:faraway':
##
## logit## The following objects are masked from 'package:ggplot2':
##
## %+%, alphaImporta a tabela ‘tab_original.xlsx’.
tbl <- readxl::read_excel('tab_original.xlsx', sheet = 'Smart PLS', col_names = TRUE)
tbl %>% head()## # A tibble: 6 x 79
## P_1 P_2 P_3 P_4 P_5 P_6 P_7 P_8 P_9 P_10 P_11 P_12 P_13
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 6 1 1 2 1 5 1 9 5 5 5 0 0
## 2 4 1 2 8 4 1 2 0 0 0 0 5 5
## 3 5 1 1 8 2 1 1 3 5 5 4 0 0
## 4 4 1 2 6 1 4 1 8 4 5 3 0 0
## 5 4 1 2 8 3 1 1 1 2 3 4 0 0
## 6 2 1 1 6 7 1 2 0 0 0 0 4 3
## # ... with 66 more variables: P_14 <dbl>, P_15 <dbl>, P_16 <dbl>, P_17 <dbl>,
## # P_18 <dbl>, P_19 <dbl>, P_20 <dbl>, P_21 <dbl>, P_22 <dbl>, P_23 <dbl>,
## # P_24 <dbl>, P_25 <dbl>, P_26 <dbl>, P_27 <dbl>, P_28 <dbl>, P_29 <dbl>,
## # P_30 <dbl>, P_31 <dbl>, P_32 <dbl>, P_33 <dbl>, P_34 <dbl>, P_35 <dbl>,
## # P_36 <dbl>, P_37 <dbl>, P_38 <dbl>, P_39 <dbl>, P_40 <dbl>, P_41 <dbl>,
## # P_42 <dbl>, P_43 <dbl>, P_44 <dbl>, P_45 <dbl>, P_46 <dbl>, P_47 <dbl>,
## # P_48 <dbl>, P_49 <dbl>, P_50 <dbl>, P_51 <dbl>, P_52 <dbl>, P_53 <dbl>,
## # P_54 <dbl>, P_55 <dbl>, P_56 <dbl>, P_57 <dbl>, P_58 <dbl>, P_59 <dbl>,
## # P_60 <dbl>, P_61 <dbl>, P_62 <dbl>, P_63 <dbl>, P_64 <dbl>, P_65 <dbl>,
## # P_66 <dbl>, P_67 <dbl>, P_68 <dbl>, P_69 <dbl>, P_70 <dbl>, P_71 <dbl>,
## # P_72 <dbl>, P_73 <dbl>, P_74 <dbl>, P_75 <dbl>, P_76 <dbl>, P_77 <dbl>,
## # P_78 <dbl>, P_79 <dbl>Exclui as variáveis dicotômicas
dic <- apply(tbl, 2 , function(x) length(unique(x)))
tbl <- tbl[dic > 2]
tbl %>% head()## # A tibble: 6 x 75
## P_1 P_3 P_4 P_5 P_6 P_8 P_9 P_10 P_11 P_12 P_13 P_14 P_15
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 6 1 2 1 5 9 5 5 5 0 0 0 1
## 2 4 2 8 4 1 0 0 0 0 5 5 3 4
## 3 5 1 8 2 1 3 5 5 4 0 0 0 4
## 4 4 2 6 1 4 8 4 5 3 0 0 0 1
## 5 4 2 8 3 1 1 2 3 4 0 0 0 4
## 6 2 1 6 7 1 0 0 0 0 4 3 5 4
## # ... with 62 more variables: P_16 <dbl>, P_17 <dbl>, P_18 <dbl>, P_19 <dbl>,
## # P_20 <dbl>, P_21 <dbl>, P_22 <dbl>, P_23 <dbl>, P_24 <dbl>, P_25 <dbl>,
## # P_26 <dbl>, P_27 <dbl>, P_28 <dbl>, P_29 <dbl>, P_30 <dbl>, P_31 <dbl>,
## # P_32 <dbl>, P_33 <dbl>, P_34 <dbl>, P_35 <dbl>, P_36 <dbl>, P_37 <dbl>,
## # P_38 <dbl>, P_39 <dbl>, P_40 <dbl>, P_41 <dbl>, P_42 <dbl>, P_43 <dbl>,
## # P_44 <dbl>, P_45 <dbl>, P_46 <dbl>, P_47 <dbl>, P_48 <dbl>, P_49 <dbl>,
## # P_50 <dbl>, P_51 <dbl>, P_53 <dbl>, P_54 <dbl>, P_55 <dbl>, P_56 <dbl>,
## # P_57 <dbl>, P_58 <dbl>, P_59 <dbl>, P_60 <dbl>, P_61 <dbl>, P_62 <dbl>,
## # P_63 <dbl>, P_64 <dbl>, P_65 <dbl>, P_66 <dbl>, P_68 <dbl>, P_69 <dbl>,
## # P_70 <dbl>, P_71 <dbl>, P_72 <dbl>, P_73 <dbl>, P_74 <dbl>, P_75 <dbl>,
## # P_76 <dbl>, P_77 <dbl>, P_78 <dbl>, P_79 <dbl>Matriz de correlação
corrgram::corrgram(tbl)## Registered S3 method overwritten by 'seriation':
## method from
## reorder.hclust gclus
Cria o modelo a ser usado no mctest
model <- lm(P_1 ~ ., data = tbl)
model ##
## Call:
## lm(formula = P_1 ~ ., data = tbl)
##
## Coefficients:
## (Intercept) P_3 P_4 P_5 P_6 P_8
## 5.284283 -0.073855 -0.148068 -0.012099 -0.051932 0.043514
## P_9 P_10 P_11 P_12 P_13 P_14
## -0.063481 -0.057544 0.069687 -0.174099 0.276800 -0.093203
## P_15 P_16 P_17 P_18 P_19 P_20
## 0.096694 -0.096822 -0.137834 0.025379 -0.001105 0.077685
## P_21 P_22 P_23 P_24 P_25 P_26
## 0.060070 0.038402 0.100166 -0.031177 -0.052533 -0.108953
## P_27 P_28 P_29 P_30 P_31 P_32
## 0.009842 0.123310 -0.016657 -0.075152 -0.051841 0.015814
## P_33 P_34 P_35 P_36 P_37 P_38
## -0.176015 -0.036312 0.064731 0.121074 -0.070185 0.073359
## P_39 P_40 P_41 P_42 P_43 P_44
## 0.025058 0.092729 -0.122805 -0.091059 0.013593 0.023774
## P_45 P_46 P_47 P_48 P_49 P_50
## -0.046259 0.023929 -0.008753 -0.036432 -0.009143 -0.077839
## P_51 P_53 P_54 P_55 P_56 P_57
## 0.048981 -0.074096 0.205010 -0.173324 0.110143 0.311208
## P_58 P_59 P_60 P_61 P_62 P_63
## -0.235184 -0.043171 0.051951 0.052429 0.105853 -0.074767
## P_64 P_65 P_66 P_68 P_69 P_70
## -0.062948 0.009030 -0.140781 0.019261 0.032148 0.016219
## P_71 P_72 P_73 P_74 P_75 P_76
## 0.011490 0.110215 0.210453 -0.146429 0.056886 -0.035356
## P_77 P_78 P_79
## -0.066597 0.092640 -0.014365Testes
Teste VIF
Apenas valores VIF sem indicador de detecção de colinearidade
imcdiag(model, method = "VIF")[[1]][,1]## P_3 P_4 P_5 P_6 P_8 P_9 P_10 P_11
## 1.280837 1.701344 1.751916 1.769911 2.150123 9.460445 9.155176 5.499082
## P_12 P_13 P_14 P_15 P_16 P_17 P_18 P_19
## 19.737630 24.172171 17.689998 2.706908 1.872850 2.268241 1.479695 2.140138
## P_20 P_21 P_22 P_23 P_24 P_25 P_26 P_27
## 2.102043 1.616254 1.456113 1.774922 1.407576 1.313954 2.451584 2.253264
## P_28 P_29 P_30 P_31 P_32 P_33 P_34 P_35
## 1.735719 1.471236 1.280464 2.065862 3.033934 2.468182 1.712952 2.854578
## P_36 P_37 P_38 P_39 P_40 P_41 P_42 P_43
## 2.629395 1.886829 2.591568 2.059173 1.922440 1.910857 1.979173 1.614549
## P_44 P_45 P_46 P_47 P_48 P_49 P_50 P_51
## 1.873505 2.345103 1.954906 2.211515 2.224966 1.654716 2.254212 2.301507
## P_53 P_54 P_55 P_56 P_57 P_58 P_59 P_60
## 4.033018 11.769492 10.733405 6.002374 26.238822 30.497281 19.617071 2.419087
## P_61 P_62 P_63 P_64 P_65 P_66 P_68 P_69
## 2.124772 2.959910 3.009846 1.810570 1.824741 2.185467 4.500665 17.488273
## P_70 P_71 P_72 P_73 P_74 P_75 P_76 P_77
## 18.322372 13.966168 5.266237 6.381689 4.399652 2.436169 3.115397 2.459926
## P_78 P_79
## 2.770801 2.586188mctest::imcdiag(model, method = "VIF", vif = 5)##
## Call:
## mctest::imcdiag(mod = model, method = "VIF", vif = 5)
##
##
## VIF Multicollinearity Diagnostics
##
## VIF detection
## P_3 1.2808 0
## P_4 1.7013 0
## P_5 1.7519 0
## P_6 1.7699 0
## P_8 2.1501 0
## P_9 9.4604 1
## P_10 9.1552 1
## P_11 5.4991 1
## P_12 19.7376 1
## P_13 24.1722 1
## P_14 17.6900 1
## P_15 2.7069 0
## P_16 1.8729 0
## P_17 2.2682 0
## P_18 1.4797 0
## P_19 2.1401 0
## P_20 2.1020 0
## P_21 1.6163 0
## P_22 1.4561 0
## P_23 1.7749 0
## P_24 1.4076 0
## P_25 1.3140 0
## P_26 2.4516 0
## P_27 2.2533 0
## P_28 1.7357 0
## P_29 1.4712 0
## P_30 1.2805 0
## P_31 2.0659 0
## P_32 3.0339 0
## P_33 2.4682 0
## P_34 1.7130 0
## P_35 2.8546 0
## P_36 2.6294 0
## P_37 1.8868 0
## P_38 2.5916 0
## P_39 2.0592 0
## P_40 1.9224 0
## P_41 1.9109 0
## P_42 1.9792 0
## P_43 1.6145 0
## P_44 1.8735 0
## P_45 2.3451 0
## P_46 1.9549 0
## P_47 2.2115 0
## P_48 2.2250 0
## P_49 1.6547 0
## P_50 2.2542 0
## P_51 2.3015 0
## P_53 4.0330 0
## P_54 11.7695 1
## P_55 10.7334 1
## P_56 6.0024 1
## P_57 26.2388 1
## P_58 30.4973 1
## P_59 19.6171 1
## P_60 2.4191 0
## P_61 2.1248 0
## P_62 2.9599 0
## P_63 3.0098 0
## P_64 1.8106 0
## P_65 1.8247 0
## P_66 2.1855 0
## P_68 4.5007 0
## P_69 17.4883 1
## P_70 18.3224 1
## P_71 13.9662 1
## P_72 5.2662 1
## P_73 6.3817 1
## P_74 4.3997 0
## P_75 2.4362 0
## P_76 3.1154 0
## P_77 2.4599 0
## P_78 2.7708 0
## P_79 2.5862 0
##
## Multicollinearity may be due to P_9 P_10 P_11 P_12 P_13 P_14 P_54 P_55 P_56 P_57 P_58 P_59 P_69 P_70 P_71 P_72 P_73 regressors
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
##
## ===================================plot(imcdiag(model, method = "VIF")[[1]][,1]) # vif plot
Testes MSA e KMO
| KMO | Interpretação |
|---|---|
| 0,9 a 1,0 | Maravilhoso |
| 0,8 a 0,9 | Meritório |
| 0,7 a 0,8 | Moderado |
| 0,6 a 0,7 | Medíocre |
| 0,5 a 0,6 | Miserável |
| menor que 0,5 | Inaceitável |
kmos <- REdaS::KMOS(tbl)
kmos##
## Kaiser-Meyer-Olkin Statistics
##
## Call: REdaS::KMOS(x = tbl)
##
## Measures of Sampling Adequacy (MSA):
## P_1 P_3 P_4 P_5 P_6 P_8 P_9 P_10
## 0.5944250 0.5709779 0.7480496 0.8836824 0.7431273 0.9169272 0.9300709 0.9242316
## P_11 P_12 P_13 P_14 P_15 P_16 P_17 P_18
## 0.9285846 0.8772543 0.8422984 0.8789042 0.8717969 0.8795182 0.8971371 0.9233417
## P_19 P_20 P_21 P_22 P_23 P_24 P_25 P_26
## 0.9376621 0.9087224 0.7175073 0.5798575 0.8610293 0.9021918 0.5431306 0.8962032
## P_27 P_28 P_29 P_30 P_31 P_32 P_33 P_34
## 0.9096462 0.9210624 0.8575319 0.7624084 0.9028105 0.9183723 0.9484675 0.9069290
## P_35 P_36 P_37 P_38 P_39 P_40 P_41 P_42
## 0.9320596 0.9490864 0.8750290 0.8542774 0.9173987 0.7956620 0.9117840 0.8782026
## P_43 P_44 P_45 P_46 P_47 P_48 P_49 P_50
## 0.9270023 0.8573811 0.8924903 0.9062378 0.7043976 0.7084762 0.8750770 0.9002754
## P_51 P_53 P_54 P_55 P_56 P_57 P_58 P_59
## 0.8943191 0.9617240 0.9206564 0.9263982 0.9343477 0.8674170 0.8334660 0.8929225
## P_60 P_61 P_62 P_63 P_64 P_65 P_66 P_68
## 0.8202236 0.8164335 0.7562597 0.7623357 0.8125158 0.8482612 0.8338416 0.9369205
## P_69 P_70 P_71 P_72 P_73 P_74 P_75 P_76
## 0.8574704 0.8533240 0.8851489 0.8735885 0.8583622 0.8863144 0.9082193 0.9287651
## P_77 P_78 P_79
## 0.9393845 0.9126783 0.8903946
##
## KMO-Criterion: 0.8880532Porcentagem de variáveis em cada faixa.
df <- data.frame(Excelente = round(100*mean(0.9 < kmos$MSA), 2),
Meritorio = round(100*mean(0.8 < kmos$MSA & kmos$MSA <= 0.9), 2),
Moderado = round(100*mean(0.7 < kmos$MSA & kmos$MSA <= 0.8), 2),
Mediocre = round(100*mean(0.6 < kmos$MSA & kmos$MSA <= 0.7), 2),
Miseravel = round(100*mean(0.5 < kmos$MSA & kmos$MSA <= 0.6), 2),
Inaceitavel = round(100*mean(kmos$MSA <= 0.5), 2))
df## Excelente Meritorio Moderado Mediocre Miseravel Inaceitavel
## 1 40 42.67 12 0 5.33 0Teste Bartlett
REdaS::bart_spher(tbl)## Bartlett's Test of Sphericity
##
## Call: REdaS::bart_spher(x = tbl)
##
## X2 = 30699.744
## df = 2775
## p-value < 2.22e-16Outros testes
- para determinacao de n. de fatores:
nfactors <- fa.parallel(tbl, plot = FALSE)## Parallel analysis suggests that the number of factors = 14 and the number of components = 10nfactors## Call: fa.parallel(x = tbl, plot = FALSE)
## Parallel analysis suggests that the number of factors = 14 and the number of components = 10
##
## Eigen Values of
## Original factors Resampled data Simulated data Original components
## 1 12.00 0.84 0.85 12.71
## 2 7.94 0.77 0.76 8.70
## 3 4.60 0.71 0.72 5.56
## 4 2.72 0.68 0.68 3.62
## 5 2.20 0.64 0.65 3.09
## 6 1.60 0.61 0.61 2.49
## 7 1.13 0.58 0.59 2.03
## 8 0.94 0.56 0.55 1.77
## 9 0.86 0.52 0.52 1.74
## 10 0.79 0.50 0.50 1.70
## 11 0.62 0.48 0.47 1.47
## 12 0.56 0.44 0.45 1.38
## 13 0.52 0.42 0.43 1.34
## 14 0.44 0.40 0.40 1.27
## Resampled components Simulated components
## 1 1.80 1.82
## 2 1.76 1.75
## 3 1.70 1.71
## 4 1.67 1.67
## 5 1.63 1.64
## 6 1.60 1.60
## 7 1.57 1.57
## 8 1.55 1.54
## 9 1.51 1.51
## 10 1.49 1.49
## 11 1.47 1.46
## 12 1.43 1.44
## 13 1.41 1.42
## 14 1.39 1.39- depois:
corMat <- cor(tbl)- lembre-se que nfactors é o resultado de fa.parallel(sua tabela) e n.obs= N, onde N é o número de observações ou linhas em sua nova tabela
nfactors <- nfactors$nfact
N <- nrow(tbl)
faPC <- fa(r = corMat, nfactors = 2, n.obs = N, rotate = "varimax")
print(faPC)## Factor Analysis using method = minres
## Call: fa(r = corMat, nfactors = 2, n.obs = N, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 h2 u2 com
## P_1 -0.13 0.03 0.0185 0.98 1.1
## P_3 0.01 -0.08 0.0060 0.99 1.0
## P_4 0.18 -0.23 0.0858 0.91 1.9
## P_5 -0.33 -0.22 0.1601 0.84 1.8
## P_6 0.01 0.27 0.0733 0.93 1.0
## P_8 0.01 0.56 0.3183 0.68 1.0
## P_9 0.21 0.84 0.7479 0.25 1.1
## P_10 0.24 0.82 0.7226 0.28 1.2
## P_11 0.25 0.74 0.6128 0.39 1.2
## P_12 0.08 -0.82 0.6833 0.32 1.0
## P_13 0.08 -0.84 0.7107 0.29 1.0
## P_14 0.11 -0.82 0.6828 0.32 1.0
## P_15 0.57 0.01 0.3285 0.67 1.0
## P_16 0.48 0.00 0.2263 0.77 1.0
## P_17 0.53 0.10 0.2917 0.71 1.1
## P_18 -0.42 0.08 0.1810 0.82 1.1
## P_19 0.62 0.09 0.3980 0.60 1.0
## P_20 0.55 0.01 0.3065 0.69 1.0
## P_21 -0.23 -0.01 0.0515 0.95 1.0
## P_22 -0.02 -0.03 0.0014 1.00 1.9
## P_23 0.38 0.17 0.1735 0.83 1.4
## P_24 0.39 0.00 0.1491 0.85 1.0
## P_25 -0.04 0.10 0.0104 0.99 1.3
## P_26 0.60 0.03 0.3636 0.64 1.0
## P_27 0.59 0.02 0.3515 0.65 1.0
## P_28 0.50 0.08 0.2553 0.74 1.1
## P_29 -0.34 0.03 0.1149 0.89 1.0
## P_30 -0.16 -0.07 0.0304 0.97 1.4
## P_31 0.55 0.00 0.2973 0.70 1.0
## P_32 0.65 0.02 0.4244 0.58 1.0
## P_33 0.64 0.10 0.4209 0.58 1.0
## P_34 0.46 -0.01 0.2155 0.78 1.0
## P_35 0.67 0.01 0.4506 0.55 1.0
## P_36 0.70 0.10 0.5003 0.50 1.0
## P_37 0.30 0.10 0.1018 0.90 1.2
## P_38 0.39 0.06 0.1543 0.85 1.0
## P_39 0.43 0.10 0.1910 0.81 1.1
## P_40 0.25 -0.09 0.0732 0.93 1.3
## P_41 0.49 0.03 0.2428 0.76 1.0
## P_42 0.46 0.03 0.2107 0.79 1.0
## P_43 0.44 -0.02 0.1968 0.80 1.0
## P_44 0.40 0.00 0.1584 0.84 1.0
## P_45 0.45 0.18 0.2375 0.76 1.3
## P_46 0.43 0.16 0.2109 0.79 1.3
## P_47 0.18 0.03 0.0338 0.97 1.0
## P_48 0.18 0.03 0.0325 0.97 1.1
## P_49 0.29 0.15 0.1083 0.89 1.5
## P_50 0.42 0.18 0.2072 0.79 1.4
## P_51 0.42 0.15 0.1987 0.80 1.3
## P_53 0.27 0.74 0.6215 0.38 1.3
## P_54 0.24 0.86 0.8050 0.20 1.2
## P_55 0.27 0.83 0.7616 0.24 1.2
## P_56 0.29 0.76 0.6590 0.34 1.3
## P_57 0.11 -0.86 0.7443 0.26 1.0
## P_58 0.13 -0.83 0.7106 0.29 1.0
## P_59 0.12 -0.84 0.7256 0.27 1.0
## P_60 0.20 -0.04 0.0409 0.96 1.1
## P_61 0.17 -0.07 0.0332 0.97 1.3
## P_62 0.12 -0.18 0.0465 0.95 1.8
## P_63 0.12 -0.15 0.0377 0.96 1.9
## P_64 0.11 -0.08 0.0184 0.98 1.9
## P_65 0.18 -0.04 0.0360 0.96 1.1
## P_66 0.17 -0.06 0.0321 0.97 1.2
## P_68 0.10 0.15 0.0309 0.97 1.8
## P_69 0.06 0.14 0.0246 0.98 1.4
## P_70 0.09 0.14 0.0265 0.97 1.7
## P_71 0.09 0.15 0.0303 0.97 1.6
## P_72 -0.02 -0.39 0.1519 0.85 1.0
## P_73 -0.03 -0.38 0.1417 0.86 1.0
## P_74 -0.02 -0.34 0.1190 0.88 1.0
## P_75 0.54 0.09 0.3052 0.69 1.1
## P_76 0.65 0.20 0.4607 0.54 1.2
## P_77 0.63 0.05 0.4014 0.60 1.0
## P_78 0.60 0.06 0.3619 0.64 1.0
## P_79 0.56 0.04 0.3106 0.69 1.0
##
## MR1 MR2
## SS loadings 10.30 10.06
## Proportion Var 0.14 0.13
## Cumulative Var 0.14 0.27
## Proportion Explained 0.51 0.49
## Cumulative Proportion 0.51 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 2775 and the objective function was 58.79 with Chi Square of 30699.74
## The degrees of freedom for the model are 2626 and the objective function was 35.25
##
## The root mean square of the residuals (RMSR) is 0.1
## The df corrected root mean square of the residuals is 0.1
##
## The harmonic number of observations is 549 with the empirical chi square 29321.74 with prob < 0
## The total number of observations was 549 with Likelihood Chi Square = 18358.41 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.403
## RMSEA index = 0.104 and the 90 % confidence intervals are 0.103 0.106
## BIC = 1793.34
## Fit based upon off diagonal values = 0.79
## Measures of factor score adequacy
## MR1 MR2
## Correlation of (regression) scores with factors 0.97 0.98
## Multiple R square of scores with factors 0.94 0.97
## Minimum correlation of possible factor scores 0.88 0.94- salvar a tabela resultante (após todas as variáveis com h2 <0,40 terem sido excluídas).
h2 <- faPC$communality # Coluna h2 da tabela acima
exclui <- mean(h2 < 0.40) > 0 # TRUE se houver h2 < 0.40
while(exclui){
tbl <- tbl[!(h2 == min(h2))] # Exclui variavel com menor h2
nfactors <- fa.parallel(tbl, plot = FALSE) # Recalcula nfactors
nfactors <- nfactors$nfact # Número de fatores
N <- nrow(tbl) # Número de linhas da nova tabela
corMat <- cor(tbl) # Recalcula correlação
faPC <- fa(r = corMat, nfactors = nfactors, n.obs = N, rotate = "varimax")
h2 <- faPC$communality # Coluna h2 da tabela acima
exclui <- mean(h2 < 0.40) > 0 # Continua enquanto houver h2 < 0.40
}## Parallel analysis suggests that the number of factors = 14 and the number of components = 10
## Parallel analysis suggests that the number of factors = 14 and the number of components = 10
## Parallel analysis suggests that the number of factors = 13 and the number of components = 10
## Parallel analysis suggests that the number of factors = 13 and the number of components = 10
## Parallel analysis suggests that the number of factors = 13 and the number of components = 10
## Parallel analysis suggests that the number of factors = 13 and the number of components = 10
## Parallel analysis suggests that the number of factors = 13 and the number of components = 10
## Parallel analysis suggests that the number of factors = 13 and the number of components = 10
## Parallel analysis suggests that the number of factors = 13 and the number of components = 10
## Parallel analysis suggests that the number of factors = 12 and the number of components = 10
## Parallel analysis suggests that the number of factors = 12 and the number of components = 10
## Parallel analysis suggests that the number of factors = 12 and the number of components = 9
## Parallel analysis suggests that the number of factors = 12 and the number of components = 9
## Parallel analysis suggests that the number of factors = 12 and the number of components = 9
## Parallel analysis suggests that the number of factors = 12 and the number of components = 9
## Parallel analysis suggests that the number of factors = 12 and the number of components = 9
## Parallel analysis suggests that the number of factors = 12 and the number of components = 9print(faPC)## Factor Analysis using method = minres
## Call: fa(r = corMat, nfactors = nfactors, n.obs = N, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 MR5 MR4 MR10 MR6 MR8 MR12 MR9 MR11 MR7
## P_4 -0.13 -0.03 0.09 -0.04 0.04 0.09 0.17 -0.01 0.05 0.59 0.09 0.07
## P_6 0.17 -0.03 0.04 -0.02 -0.08 0.08 0.02 -0.03 0.00 -0.67 0.02 -0.01
## P_8 0.47 0.15 -0.01 -0.07 -0.09 -0.01 0.05 0.07 0.05 -0.53 0.04 0.15
## P_9 0.84 0.11 0.15 0.09 -0.10 0.10 0.05 0.07 -0.01 -0.02 -0.16 0.27
## P_10 0.83 0.09 0.16 0.09 -0.05 0.11 0.08 0.05 -0.02 -0.02 -0.06 0.32
## P_11 0.78 0.07 0.13 0.11 -0.01 0.11 0.10 0.09 0.00 0.06 -0.03 0.30
## P_12 -0.80 -0.06 0.02 0.04 0.03 0.00 0.04 0.01 0.03 0.14 0.51 -0.01
## P_13 -0.81 -0.07 0.03 0.04 0.01 -0.01 0.03 0.03 0.02 0.15 0.50 0.01
## P_14 -0.80 -0.05 0.06 0.06 0.01 -0.01 0.03 0.04 0.04 0.14 0.51 -0.03
## P_15 0.03 0.00 0.54 0.07 0.06 0.15 0.02 0.37 -0.01 0.03 0.02 -0.04
## P_17 0.11 0.08 0.54 0.03 0.03 0.10 0.05 0.33 -0.04 0.02 0.05 -0.02
## P_19 0.09 0.05 0.59 0.10 0.03 0.23 -0.01 0.15 0.13 -0.02 0.03 0.03
## P_20 0.01 -0.02 0.69 0.04 0.03 0.07 0.05 0.05 0.07 0.00 -0.04 0.04
## P_26 0.04 0.03 0.33 0.16 0.07 0.13 0.11 0.13 0.69 0.04 -0.01 -0.01
## P_27 0.01 0.05 0.37 0.24 0.00 0.16 0.06 0.06 0.52 0.04 0.03 -0.02
## P_28 0.09 0.03 0.39 0.08 -0.03 0.08 0.05 0.05 0.46 -0.01 0.06 0.08
## P_31 0.00 0.01 0.23 0.20 0.09 0.20 0.03 0.19 0.60 -0.01 -0.02 -0.03
## P_32 0.03 -0.03 0.79 0.08 0.03 0.13 0.02 -0.01 0.13 0.02 -0.02 -0.02
## P_33 0.09 -0.01 0.61 0.01 -0.06 0.37 0.11 0.02 0.17 -0.04 0.02 0.04
## P_35 0.03 -0.04 0.68 0.14 -0.02 0.19 0.03 0.08 0.20 0.01 0.04 -0.04
## P_36 0.11 -0.02 0.66 0.18 0.04 0.21 0.10 0.05 0.17 0.05 -0.01 0.07
## P_37 0.09 0.01 0.08 0.65 0.01 -0.02 0.06 0.10 0.04 -0.01 0.04 -0.01
## P_38 0.04 0.01 0.11 0.79 -0.01 0.04 -0.04 0.11 0.14 0.03 -0.05 0.00
## P_39 0.09 0.03 0.12 0.66 0.01 0.09 0.04 0.09 0.20 0.04 0.03 0.01
## P_40 -0.11 -0.01 0.06 0.65 0.02 0.05 -0.09 0.14 -0.02 0.03 -0.08 -0.08
## P_41 0.05 0.04 0.22 0.15 0.11 0.12 0.08 0.63 0.09 0.02 0.00 0.00
## P_42 0.05 0.01 0.21 0.12 0.10 0.11 0.03 0.66 0.09 0.00 0.02 -0.01
## P_44 0.01 -0.02 0.11 0.21 0.06 0.07 0.05 0.61 0.12 -0.03 -0.01 0.04
## P_45 0.18 -0.03 0.21 0.39 0.12 0.05 0.45 0.04 0.12 -0.06 0.07 0.13
## P_46 0.14 0.04 0.23 0.21 0.10 0.13 0.49 -0.04 0.11 -0.10 0.06 0.10
## P_47 0.03 -0.03 0.03 -0.10 0.07 0.05 0.74 0.08 0.00 0.11 -0.05 -0.05
## P_48 0.02 0.00 -0.02 -0.04 0.05 0.09 0.73 0.08 0.00 0.11 -0.02 -0.06
## P_50 0.17 0.06 0.17 0.49 0.04 0.03 0.33 0.02 0.10 -0.11 0.21 0.19
## P_51 0.14 0.05 0.12 0.42 0.11 0.03 0.48 0.02 0.17 -0.10 0.12 0.14
## P_53 0.75 0.04 0.14 0.10 -0.05 0.13 0.18 0.04 0.09 -0.08 0.15 -0.12
## P_54 0.88 0.09 0.17 0.07 -0.07 0.09 0.10 0.03 0.06 -0.07 0.22 -0.02
## P_55 0.87 0.06 0.17 0.07 -0.03 0.08 0.11 0.08 0.05 -0.06 0.26 0.08
## P_56 0.80 0.05 0.12 0.15 0.03 0.12 0.12 0.06 0.10 -0.02 0.27 0.09
## P_57 -0.86 -0.05 0.05 0.01 0.02 0.07 0.06 0.03 0.02 0.12 0.02 0.40
## P_58 -0.84 -0.06 0.05 0.02 0.02 0.08 0.07 0.04 0.00 0.11 0.01 0.44
## P_59 -0.85 -0.06 0.07 0.01 0.00 0.07 0.04 0.06 -0.03 0.10 0.03 0.41
## P_60 0.01 0.16 0.02 0.10 0.68 0.06 -0.04 0.03 0.03 0.06 0.02 0.07
## P_61 -0.02 0.08 0.02 0.17 0.66 0.03 0.04 0.00 -0.05 0.05 0.03 0.01
## P_62 -0.12 0.00 0.03 -0.12 0.69 -0.04 0.12 0.08 0.09 -0.01 -0.05 -0.06
## P_63 -0.10 -0.01 0.06 -0.15 0.72 -0.01 0.11 0.12 -0.03 0.01 -0.05 -0.10
## P_66 -0.01 0.11 -0.01 0.05 0.62 0.02 0.05 0.04 0.06 0.05 0.03 0.06
## P_68 0.01 0.82 0.00 -0.01 0.26 0.03 0.03 0.03 0.03 0.00 0.02 0.00
## P_69 0.00 0.88 -0.04 0.01 0.26 0.03 0.00 -0.01 0.02 0.07 -0.03 0.14
## P_70 0.00 0.88 -0.03 0.01 0.27 0.06 0.00 0.00 0.03 0.07 -0.05 0.16
## P_71 0.02 0.88 -0.01 0.00 0.27 0.04 -0.01 0.00 0.02 0.08 -0.04 0.15
## P_72 -0.23 -0.78 -0.04 -0.02 0.17 0.02 0.02 -0.02 0.02 0.08 -0.08 0.14
## P_73 -0.19 -0.82 -0.04 -0.06 0.16 0.02 -0.01 0.01 0.02 0.10 -0.02 0.14
## P_74 -0.16 -0.78 -0.04 -0.01 0.14 0.03 0.00 -0.02 -0.03 0.12 0.02 0.14
## P_75 0.09 -0.04 0.31 0.03 -0.01 0.64 0.14 0.03 0.07 0.01 0.02 0.03
## P_76 0.19 0.07 0.47 0.06 0.00 0.58 0.11 0.09 0.05 -0.03 0.04 0.10
## P_77 0.04 0.04 0.39 0.01 0.10 0.60 0.06 0.18 0.16 -0.04 0.01 -0.01
## P_78 0.06 0.01 0.30 0.06 0.02 0.73 0.04 0.10 0.18 0.03 -0.03 -0.04
## P_79 0.04 0.03 0.30 0.07 0.02 0.68 0.03 0.12 0.06 0.03 0.00 0.02
## h2 u2 com
## P_4 0.43 0.573 1.5
## P_6 0.50 0.504 1.2
## P_8 0.57 0.426 2.6
## P_9 0.86 0.135 1.5
## P_10 0.86 0.141 1.5
## P_11 0.76 0.235 1.6
## P_12 0.92 0.077 1.8
## P_13 0.94 0.064 1.8
## P_14 0.93 0.068 1.8
## P_15 0.46 0.543 2.0
## P_17 0.43 0.567 2.0
## P_19 0.46 0.541 1.7
## P_20 0.49 0.508 1.1
## P_26 0.67 0.332 1.9
## P_27 0.51 0.491 2.6
## P_28 0.40 0.599 2.4
## P_31 0.53 0.467 2.1
## P_32 0.67 0.331 1.1
## P_33 0.56 0.442 2.0
## P_35 0.56 0.437 1.5
## P_36 0.58 0.424 1.7
## P_37 0.45 0.550 1.2
## P_38 0.67 0.330 1.2
## P_39 0.52 0.481 1.4
## P_40 0.48 0.517 1.3
## P_41 0.52 0.480 1.6
## P_42 0.52 0.477 1.4
## P_44 0.46 0.544 1.5
## P_45 0.49 0.510 3.5
## P_46 0.43 0.575 2.8
## P_47 0.59 0.407 1.2
## P_48 0.57 0.428 1.1
## P_50 0.51 0.485 3.5
## P_51 0.53 0.471 3.2
## P_53 0.70 0.303 1.5
## P_54 0.90 0.103 1.3
## P_55 0.89 0.106 1.4
## P_56 0.81 0.194 1.5
## P_57 0.93 0.068 1.5
## P_58 0.94 0.059 1.6
## P_59 0.92 0.077 1.5
## P_60 0.52 0.478 1.2
## P_61 0.48 0.520 1.2
## P_62 0.55 0.452 1.3
## P_63 0.60 0.405 1.3
## P_66 0.42 0.583 1.2
## P_68 0.75 0.251 1.2
## P_69 0.87 0.128 1.3
## P_70 0.88 0.120 1.3
## P_71 0.88 0.125 1.3
## P_72 0.72 0.281 1.4
## P_73 0.78 0.223 1.3
## P_74 0.70 0.304 1.3
## P_75 0.55 0.451 1.7
## P_76 0.63 0.367 2.5
## P_77 0.59 0.411 2.2
## P_78 0.68 0.321 1.6
## P_79 0.57 0.427 1.5
##
## MR1 MR3 MR2 MR5 MR4 MR10 MR6 MR8 MR12 MR9 MR11
## SS loadings 9.47 5.05 4.85 2.99 2.80 2.71 2.14 1.75 1.74 1.33 1.14
## Proportion Var 0.16 0.09 0.08 0.05 0.05 0.05 0.04 0.03 0.03 0.02 0.02
## Cumulative Var 0.16 0.25 0.33 0.39 0.43 0.48 0.52 0.55 0.58 0.60 0.62
## Proportion Explained 0.26 0.14 0.13 0.08 0.08 0.07 0.06 0.05 0.05 0.04 0.03
## Cumulative Proportion 0.26 0.39 0.52 0.60 0.68 0.75 0.81 0.86 0.90 0.94 0.97
## MR7
## SS loadings 1.13
## Proportion Var 0.02
## Cumulative Var 0.64
## Proportion Explained 0.03
## Cumulative Proportion 1.00
##
## Mean item complexity = 1.7
## Test of the hypothesis that 12 factors are sufficient.
##
## The degrees of freedom for the null model are 1653 and the objective function was 51.87 with Chi Square of 27380.39
## The degrees of freedom for the model are 1023 and the objective function was 7.36
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic number of observations is 549 with the empirical chi square 893.79 with prob < 1
## The total number of observations was 549 with Likelihood Chi Square = 3827.14 with prob < 9.699991e-319
##
## Tucker Lewis Index of factoring reliability = 0.821
## RMSEA index = 0.071 and the 90 % confidence intervals are 0.068 0.073
## BIC = -2626.04
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## MR1 MR3 MR2 MR5 MR4 MR10
## Correlation of (regression) scores with factors 0.99 0.98 0.92 0.91 0.92 0.89
## Multiple R square of scores with factors 0.98 0.96 0.84 0.84 0.85 0.79
## Minimum correlation of possible factor scores 0.96 0.92 0.68 0.67 0.70 0.58
## MR6 MR8 MR12 MR9 MR11 MR7
## Correlation of (regression) scores with factors 0.89 0.85 0.85 0.84 0.95 0.94
## Multiple R square of scores with factors 0.80 0.73 0.72 0.70 0.90 0.88
## Minimum correlation of possible factor scores 0.59 0.45 0.43 0.41 0.79 0.75Cria o scree plot
fa.parallel(tbl)
## Parallel analysis suggests that the number of factors = 12 and the number of components = 9- executar fa.diagram(faPC) para identificar os fatores com suas respectivas variáveis, onde faPC é o resultante da AFE sem as variáveis com h2 <0,40.
fa.diagram(faPC)