1 Main analysis
Last review on January 4, 2022.
load(url("https://osf.io/s8rxb/download"))#Packages
pacman::p_load(tidyverse, #enrironment
arsenal,
knitr,
psych) #classical testR Notebook - Exploratory analysis - DA
Luis Anunciação
Note: This is the R markdown of the manuscript “An Exploratory Analysis of the Internal Structure of Test Through a Multi-methods Exploratory Approach of the ASQ:SE in Brazil”. The first set of chunks reproduce a previous published paper (“Confirmatory analysis and normative tables for the Brazilian Ages and Stages Questionnaires: Social–Emotional”) that used the same dataframe.
Click run to reproduce all analyzes.
If you have any questions or queries, please reach me out at luisfca@puc-rio.br
last updated: 04 January, 2022
2 Previous Wiley
2.1 Descriptives
Page 3
| 1 (N=11291) | 2 (N=11040) | Total (N=22331) | p value | |
|---|---|---|---|---|
| score | < 0.001 | |||
| Mean (SD) | 44.823 (36.665) | 34.017 (30.441) | 39.481 (34.161) | |
| Range | 0.000 - 275.000 | 0.000 - 290.000 | 0.000 - 290.000 |
ds_60 %>%
tableby(sex ~ score, data = .) %>%
summary()
2.2 IRT
cfa60 <- '
F1 = 2, 5, 6, 7, 9, 11, 12, 13, 15, 16, 17, 20, 22, 23, 24, 25, 26, 30, 31, 32
F2 = 1, 3, 4, 8, 10, 14, 18, 19, 21, 27, 28, 29
COV = F1*F2'https://onlinelibrary.wiley.com/doi/10.1111/cch.12649
Months 60
M2 1,035.145 (current = 1053.881)
df 431
P <0.001
RMSEA 0.05
SRMSR 0.08
TLI 0.91 (0.93)
CFI 0.92 (0.94)
mirt::mirt(ds_60_random[-c(1:4,37)] ,
cfa60,
itemtype= 'graded', method = 'MHRM') %>%
mirt::M2(.)"q_1" re-mapped to ensure all categories have a distance of 1
"q_2" re-mapped to ensure all categories have a distance of 1
"q_3" re-mapped to ensure all categories have a distance of 1
"q_4" re-mapped to ensure all categories have a distance of 1
"q_5" re-mapped to ensure all categories have a distance of 1
"q_6" re-mapped to ensure all categories have a distance of 1
"q_7" re-mapped to ensure all categories have a distance of 1
"q_8" re-mapped to ensure all categories have a distance of 1
"q_9" re-mapped to ensure all categories have a distance of 1
"q_10" re-mapped to ensure all categories have a distance of 1
"q_11" re-mapped to ensure all categories have a distance of 1
"q_12" re-mapped to ensure all categories have a distance of 1
"q_13" re-mapped to ensure all categories have a distance of 1
"q_14" re-mapped to ensure all categories have a distance of 1
"q_15" re-mapped to ensure all categories have a distance of 1
"q_16" re-mapped to ensure all categories have a distance of 1
"q_17" re-mapped to ensure all categories have a distance of 1
"q_18" re-mapped to ensure all categories have a distance of 1
"q_19" re-mapped to ensure all categories have a distance of 1
"q_20" re-mapped to ensure all categories have a distance of 1
"q_21" re-mapped to ensure all categories have a distance of 1
"q_22" re-mapped to ensure all categories have a distance of 1
"q_23" re-mapped to ensure all categories have a distance of 1
"q_24" re-mapped to ensure all categories have a distance of 1
"q_25" re-mapped to ensure all categories have a distance of 1
"q_26" re-mapped to ensure all categories have a distance of 1
"q_27" re-mapped to ensure all categories have a distance of 1
"q_28" re-mapped to ensure all categories have a distance of 1
"q_29" re-mapped to ensure all categories have a distance of 1
"q_30" re-mapped to ensure all categories have a distance of 1
"q_31" re-mapped to ensure all categories have a distance of 1
"q_32" re-mapped to ensure all categories have a distance of 1
Stage 1 = 1, LL = -9215.6, AR(0.55) = [0.45], Max-Change = 0.2000
Stage 1 = 2, LL = -9157.9, AR(0.55) = [0.46], Max-Change = 0.2000
Stage 1 = 3, LL = -9072.9, AR(0.55) = [0.44], Max-Change = 0.2000
Stage 1 = 4, LL = -9053.6, AR(0.55) = [0.45], Max-Change = 0.2000
Stage 1 = 5, LL = -8967.0, AR(0.55) = [0.47], Max-Change = 0.2000
Stage 1 = 6, LL = -8948.9, AR(0.55) = [0.48], Max-Change = 0.1697
Stage 1 = 7, LL = -8898.4, AR(0.55) = [0.44], Max-Change = 0.1808
Stage 1 = 8, LL = -8861.5, AR(0.55) = [0.41], Max-Change = 0.1560
Stage 1 = 9, LL = -8859.3, AR(0.55) = [0.41], Max-Change = 0.1445
Stage 1 = 10, LL = -8824.1, AR(0.55) = [0.43], Max-Change = 0.1728
Stage 1 = 11, LL = -8770.1, AR(0.55) = [0.42], Max-Change = 0.1109
Stage 1 = 12, LL = -8741.1, AR(0.55) = [0.45], Max-Change = 0.1587
Stage 1 = 13, LL = -8716.6, AR(0.55) = [0.42], Max-Change = 0.1827
Stage 1 = 14, LL = -8717.8, AR(0.55) = [0.40], Max-Change = 0.1243
Stage 1 = 15, LL = -8697.4, AR(0.55) = [0.39], Max-Change = 0.1197
Stage 1 = 16, LL = -8701.6, AR(0.55) = [0.38], Max-Change = 0.1722
Stage 1 = 17, LL = -8683.0, AR(0.55) = [0.38], Max-Change = 0.1651
Stage 1 = 18, LL = -8686.3, AR(0.55) = [0.40], Max-Change = 0.0948
Stage 1 = 19, LL = -8669.1, AR(0.55) = [0.39], Max-Change = 0.1062
Stage 1 = 20, LL = -8676.2, AR(0.55) = [0.41], Max-Change = 0.1063
Stage 1 = 21, LL = -8708.0, AR(0.55) = [0.39], Max-Change = 0.1098
Stage 1 = 22, LL = -8665.9, AR(0.55) = [0.43], Max-Change = 0.1057
Stage 1 = 23, LL = -8680.2, AR(0.55) = [0.42], Max-Change = 0.0653
Stage 1 = 24, LL = -8646.8, AR(0.55) = [0.35], Max-Change = 0.0774
Stage 1 = 25, LL = -8643.6, AR(0.55) = [0.38], Max-Change = 0.0736
Stage 1 = 26, LL = -8602.0, AR(0.55) = [0.39], Max-Change = 0.0494
Stage 1 = 27, LL = -8608.5, AR(0.55) = [0.39], Max-Change = 0.1006
Stage 1 = 28, LL = -8610.0, AR(0.55) = [0.41], Max-Change = 0.0902
Stage 1 = 29, LL = -8657.5, AR(0.55) = [0.37], Max-Change = 0.0975
Stage 1 = 30, LL = -8620.8, AR(0.55) = [0.36], Max-Change = 0.0809
Stage 1 = 31, LL = -8606.2, AR(0.55) = [0.38], Max-Change = 0.0803
Stage 1 = 32, LL = -8642.7, AR(0.55) = [0.37], Max-Change = 0.1665
Stage 1 = 33, LL = -8634.0, AR(0.55) = [0.37], Max-Change = 0.0872
Stage 1 = 34, LL = -8630.8, AR(0.55) = [0.36], Max-Change = 0.0913
Stage 1 = 35, LL = -8596.7, AR(0.55) = [0.38], Max-Change = 0.1123
Stage 1 = 36, LL = -8588.1, AR(0.55) = [0.36], Max-Change = 0.0761
Stage 1 = 37, LL = -8587.0, AR(0.55) = [0.37], Max-Change = 0.0841
Stage 1 = 38, LL = -8568.0, AR(0.55) = [0.39], Max-Change = 0.0563
Stage 1 = 39, LL = -8579.3, AR(0.55) = [0.35], Max-Change = 0.0718
Stage 1 = 40, LL = -8573.8, AR(0.55) = [0.32], Max-Change = 0.0513
Stage 1 = 41, LL = -8574.9, AR(0.55) = [0.38], Max-Change = 0.0933
Stage 1 = 42, LL = -8553.5, AR(0.55) = [0.38], Max-Change = 0.0750
Stage 1 = 43, LL = -8580.2, AR(0.55) = [0.39], Max-Change = 0.1630
Stage 1 = 44, LL = -8573.2, AR(0.55) = [0.39], Max-Change = 0.1143
Stage 1 = 45, LL = -8563.9, AR(0.55) = [0.38], Max-Change = 0.0879
Stage 1 = 46, LL = -8569.6, AR(0.55) = [0.38], Max-Change = 0.0929
Stage 1 = 47, LL = -8580.6, AR(0.55) = [0.30], Max-Change = 0.0935
Stage 1 = 48, LL = -8558.9, AR(0.55) = [0.36], Max-Change = 0.0848
Stage 1 = 49, LL = -8595.3, AR(0.55) = [0.36], Max-Change = 0.1879
Stage 1 = 50, LL = -8561.2, AR(0.55) = [0.36], Max-Change = 0.0818
Stage 1 = 51, LL = -8514.2, AR(0.55) = [0.32], Max-Change = 0.0797
Stage 1 = 52, LL = -8554.9, AR(0.55) = [0.38], Max-Change = 0.1318
Stage 1 = 53, LL = -8533.1, AR(0.55) = [0.35], Max-Change = 0.1427
Stage 1 = 54, LL = -8566.2, AR(0.55) = [0.37], Max-Change = 0.1792
Stage 1 = 55, LL = -8537.2, AR(0.55) = [0.35], Max-Change = 0.0997
Stage 1 = 56, LL = -8541.4, AR(0.55) = [0.39], Max-Change = 0.0908
Stage 1 = 57, LL = -8479.3, AR(0.55) = [0.37], Max-Change = 0.0855
Stage 1 = 58, LL = -8526.8, AR(0.55) = [0.35], Max-Change = 0.1159
Stage 1 = 59, LL = -8530.9, AR(0.55) = [0.37], Max-Change = 0.1005
Stage 1 = 60, LL = -8530.7, AR(0.55) = [0.38], Max-Change = 0.1119
Stage 1 = 61, LL = -8506.0, AR(0.55) = [0.34], Max-Change = 0.0849
Stage 1 = 62, LL = -8488.0, AR(0.55) = [0.31], Max-Change = 0.1540
Stage 1 = 63, LL = -8459.9, AR(0.55) = [0.35], Max-Change = 0.0668
Stage 1 = 64, LL = -8475.4, AR(0.55) = [0.37], Max-Change = 0.0897
Stage 1 = 65, LL = -8490.8, AR(0.55) = [0.34], Max-Change = 0.0885
Stage 1 = 66, LL = -8469.4, AR(0.55) = [0.31], Max-Change = 0.1280
Stage 1 = 67, LL = -8482.2, AR(0.55) = [0.33], Max-Change = 0.0850
Stage 1 = 68, LL = -8523.8, AR(0.55) = [0.33], Max-Change = 0.0659
Stage 1 = 69, LL = -8485.2, AR(0.55) = [0.32], Max-Change = 0.1022
Stage 1 = 70, LL = -8468.9, AR(0.55) = [0.35], Max-Change = 0.0563
Stage 1 = 71, LL = -8457.2, AR(0.55) = [0.32], Max-Change = 0.0640
Stage 1 = 72, LL = -8473.8, AR(0.55) = [0.33], Max-Change = 0.0641
Stage 1 = 73, LL = -8517.7, AR(0.55) = [0.32], Max-Change = 0.0733
Stage 1 = 74, LL = -8471.0, AR(0.55) = [0.35], Max-Change = 0.1493
Stage 1 = 75, LL = -8464.6, AR(0.55) = [0.34], Max-Change = 0.0945
Stage 1 = 76, LL = -8542.2, AR(0.55) = [0.30], Max-Change = 0.1221
Stage 1 = 77, LL = -8526.0, AR(0.55) = [0.30], Max-Change = 0.1109
Stage 1 = 78, LL = -8523.5, AR(0.55) = [0.35], Max-Change = 0.0598
Stage 1 = 79, LL = -8480.5, AR(0.55) = [0.34], Max-Change = 0.0750
Stage 1 = 80, LL = -8479.6, AR(0.55) = [0.32], Max-Change = 0.1160
Stage 1 = 81, LL = -8523.4, AR(0.55) = [0.32], Max-Change = 0.0876
Stage 1 = 82, LL = -8511.7, AR(0.55) = [0.31], Max-Change = 0.0755
Stage 1 = 83, LL = -8529.9, AR(0.55) = [0.37], Max-Change = 0.0873
Stage 1 = 84, LL = -8559.4, AR(0.55) = [0.33], Max-Change = 0.1153
Stage 1 = 85, LL = -8550.4, AR(0.55) = [0.35], Max-Change = 0.1032
Stage 1 = 86, LL = -8521.0, AR(0.55) = [0.36], Max-Change = 0.1452
Stage 1 = 87, LL = -8483.9, AR(0.55) = [0.34], Max-Change = 0.0874
Stage 1 = 88, LL = -8522.6, AR(0.55) = [0.34], Max-Change = 0.0579
Stage 1 = 89, LL = -8510.0, AR(0.55) = [0.35], Max-Change = 0.0821
Stage 1 = 90, LL = -8501.3, AR(0.55) = [0.33], Max-Change = 0.0541
Stage 1 = 91, LL = -8487.3, AR(0.55) = [0.32], Max-Change = 0.0805
Stage 1 = 92, LL = -8510.4, AR(0.55) = [0.33], Max-Change = 0.0626
Stage 1 = 93, LL = -8509.3, AR(0.55) = [0.37], Max-Change = 0.0652
Stage 1 = 94, LL = -8522.7, AR(0.55) = [0.34], Max-Change = 0.0955
Stage 1 = 95, LL = -8518.4, AR(0.55) = [0.37], Max-Change = 0.1026
Stage 1 = 96, LL = -8487.1, AR(0.55) = [0.36], Max-Change = 0.0783
Stage 1 = 97, LL = -8476.3, AR(0.55) = [0.28], Max-Change = 0.1297
Stage 1 = 98, LL = -8490.2, AR(0.55) = [0.33], Max-Change = 0.0676
Stage 1 = 99, LL = -8502.1, AR(0.55) = [0.34], Max-Change = 0.1141
Stage 1 = 100, LL = -8511.0, AR(0.55) = [0.33], Max-Change = 0.1144
Stage 1 = 101, LL = -8487.4, AR(0.55) = [0.34], Max-Change = 0.0700
Stage 1 = 102, LL = -8490.4, AR(0.55) = [0.33], Max-Change = 0.1316
Stage 1 = 103, LL = -8517.2, AR(0.55) = [0.35], Max-Change = 0.1220
Stage 1 = 104, LL = -8501.9, AR(0.55) = [0.36], Max-Change = 0.0597
Stage 1 = 105, LL = -8503.0, AR(0.55) = [0.34], Max-Change = 0.1281
Stage 1 = 106, LL = -8512.1, AR(0.55) = [0.34], Max-Change = 0.1460
Stage 1 = 107, LL = -8521.2, AR(0.55) = [0.35], Max-Change = 0.0860
Stage 1 = 108, LL = -8561.0, AR(0.55) = [0.35], Max-Change = 0.0902
Stage 1 = 109, LL = -8528.3, AR(0.55) = [0.35], Max-Change = 0.0717
Stage 1 = 110, LL = -8529.4, AR(0.55) = [0.37], Max-Change = 0.0701
Stage 1 = 111, LL = -8551.4, AR(0.55) = [0.34], Max-Change = 0.0944
Stage 1 = 112, LL = -8526.6, AR(0.55) = [0.33], Max-Change = 0.0750
Stage 1 = 113, LL = -8531.2, AR(0.55) = [0.34], Max-Change = 0.0590
Stage 1 = 114, LL = -8501.2, AR(0.55) = [0.36], Max-Change = 0.0568
Stage 1 = 115, LL = -8547.9, AR(0.55) = [0.37], Max-Change = 0.0820
Stage 1 = 116, LL = -8552.2, AR(0.55) = [0.35], Max-Change = 0.0481
Stage 1 = 117, LL = -8498.2, AR(0.55) = [0.36], Max-Change = 0.0999
Stage 1 = 118, LL = -8521.7, AR(0.55) = [0.36], Max-Change = 0.1197
Stage 1 = 119, LL = -8481.4, AR(0.55) = [0.32], Max-Change = 0.1145
Stage 1 = 120, LL = -8494.9, AR(0.55) = [0.31], Max-Change = 0.1305
Stage 1 = 121, LL = -8464.2, AR(0.55) = [0.36], Max-Change = 0.0903
Stage 1 = 122, LL = -8490.1, AR(0.55) = [0.37], Max-Change = 0.1055
Stage 1 = 123, LL = -8516.8, AR(0.55) = [0.33], Max-Change = 0.0603
Stage 1 = 124, LL = -8537.3, AR(0.55) = [0.32], Max-Change = 0.1020
Stage 1 = 125, LL = -8512.2, AR(0.55) = [0.29], Max-Change = 0.1379
Stage 1 = 126, LL = -8508.2, AR(0.55) = [0.40], Max-Change = 0.0832
Stage 1 = 127, LL = -8515.8, AR(0.55) = [0.37], Max-Change = 0.1325
Stage 1 = 128, LL = -8481.5, AR(0.55) = [0.33], Max-Change = 0.0749
Stage 1 = 129, LL = -8471.6, AR(0.55) = [0.34], Max-Change = 0.0803
Stage 1 = 130, LL = -8500.5, AR(0.55) = [0.33], Max-Change = 0.0996
Stage 1 = 131, LL = -8502.7, AR(0.55) = [0.32], Max-Change = 0.0915
Stage 1 = 132, LL = -8542.1, AR(0.55) = [0.35], Max-Change = 0.0749
Stage 1 = 133, LL = -8514.7, AR(0.55) = [0.36], Max-Change = 0.0962
Stage 1 = 134, LL = -8529.6, AR(0.55) = [0.36], Max-Change = 0.0910
Stage 1 = 135, LL = -8500.9, AR(0.55) = [0.31], Max-Change = 0.0669
Stage 1 = 136, LL = -8485.1, AR(0.55) = [0.33], Max-Change = 0.1216
Stage 1 = 137, LL = -8483.6, AR(0.55) = [0.29], Max-Change = 0.1260
Stage 1 = 138, LL = -8481.8, AR(0.55) = [0.34], Max-Change = 0.0723
Stage 1 = 139, LL = -8478.0, AR(0.55) = [0.31], Max-Change = 0.0860
Stage 1 = 140, LL = -8454.5, AR(0.55) = [0.35], Max-Change = 0.0854
Stage 1 = 141, LL = -8476.1, AR(0.55) = [0.35], Max-Change = 0.0715
Stage 1 = 142, LL = -8522.8, AR(0.55) = [0.30], Max-Change = 0.0657
Stage 1 = 143, LL = -8504.2, AR(0.55) = [0.34], Max-Change = 0.1009
Stage 1 = 144, LL = -8504.4, AR(0.55) = [0.33], Max-Change = 0.0711
Stage 1 = 145, LL = -8503.1, AR(0.55) = [0.33], Max-Change = 0.0509
Stage 1 = 146, LL = -8503.9, AR(0.55) = [0.34], Max-Change = 0.0733
Stage 1 = 147, LL = -8533.7, AR(0.55) = [0.35], Max-Change = 0.0442
Stage 1 = 148, LL = -8479.9, AR(0.55) = [0.30], Max-Change = 0.0576
Stage 1 = 149, LL = -8488.5, AR(0.55) = [0.35], Max-Change = 0.0799
Stage 1 = 150, LL = -8506.2, AR(0.50) = [0.39], Max-Change = 0.1716
Stage 2 = 1, LL = -8503.6, AR(0.50) = [0.34], Max-Change = 0.0484
Stage 2 = 2, LL = -8531.1, AR(0.50) = [0.33], Max-Change = 0.0894
Stage 2 = 3, LL = -8532.8, AR(0.50) = [0.38], Max-Change = 0.0605
Stage 2 = 4, LL = -8485.6, AR(0.50) = [0.36], Max-Change = 0.1049
Stage 2 = 5, LL = -8493.1, AR(0.50) = [0.38], Max-Change = 0.1103
Stage 2 = 6, LL = -8483.3, AR(0.50) = [0.34], Max-Change = 0.1016
Stage 2 = 7, LL = -8497.5, AR(0.50) = [0.35], Max-Change = 0.1173
Stage 2 = 8, LL = -8494.2, AR(0.50) = [0.30], Max-Change = 0.0992
Stage 2 = 9, LL = -8472.1, AR(0.50) = [0.36], Max-Change = 0.0721
Stage 2 = 10, LL = -8475.6, AR(0.50) = [0.34], Max-Change = 0.0685
Stage 2 = 11, LL = -8479.3, AR(0.50) = [0.36], Max-Change = 0.0962
Stage 2 = 12, LL = -8490.6, AR(0.50) = [0.36], Max-Change = 0.0719
Stage 2 = 13, LL = -8461.0, AR(0.50) = [0.36], Max-Change = 0.0677
Stage 2 = 14, LL = -8478.1, AR(0.50) = [0.33], Max-Change = 0.0660
Stage 2 = 15, LL = -8470.0, AR(0.50) = [0.34], Max-Change = 0.0802
Stage 2 = 16, LL = -8461.6, AR(0.50) = [0.35], Max-Change = 0.0774
Stage 2 = 17, LL = -8496.3, AR(0.50) = [0.36], Max-Change = 0.1212
Stage 2 = 18, LL = -8509.0, AR(0.50) = [0.33], Max-Change = 0.0479
Stage 2 = 19, LL = -8468.7, AR(0.50) = [0.31], Max-Change = 0.0741
Stage 2 = 20, LL = -8462.2, AR(0.50) = [0.38], Max-Change = 0.0854
Stage 2 = 21, LL = -8454.9, AR(0.50) = [0.32], Max-Change = 0.0854
Stage 2 = 22, LL = -8487.8, AR(0.50) = [0.36], Max-Change = 0.0692
Stage 2 = 23, LL = -8491.6, AR(0.50) = [0.35], Max-Change = 0.1064
Stage 2 = 24, LL = -8488.6, AR(0.50) = [0.38], Max-Change = 0.0555
Stage 2 = 25, LL = -8476.4, AR(0.50) = [0.32], Max-Change = 0.0496
Stage 2 = 26, LL = -8472.9, AR(0.50) = [0.35], Max-Change = 0.0998
Stage 2 = 27, LL = -8474.6, AR(0.50) = [0.34], Max-Change = 0.0494
Stage 2 = 28, LL = -8462.5, AR(0.50) = [0.38], Max-Change = 0.0605
Stage 2 = 29, LL = -8507.1, AR(0.50) = [0.30], Max-Change = 0.1436
Stage 2 = 30, LL = -8492.3, AR(0.50) = [0.37], Max-Change = 0.0635
Stage 2 = 31, LL = -8468.3, AR(0.50) = [0.35], Max-Change = 0.1351
Stage 2 = 32, LL = -8454.4, AR(0.50) = [0.33], Max-Change = 0.1084
Stage 2 = 33, LL = -8480.0, AR(0.50) = [0.35], Max-Change = 0.1029
Stage 2 = 34, LL = -8478.5, AR(0.50) = [0.36], Max-Change = 0.0925
Stage 2 = 35, LL = -8454.5, AR(0.50) = [0.34], Max-Change = 0.0900
Stage 2 = 36, LL = -8512.8, AR(0.50) = [0.34], Max-Change = 0.1505
Stage 2 = 37, LL = -8499.8, AR(0.50) = [0.31], Max-Change = 0.1028
Stage 2 = 38, LL = -8558.7, AR(0.50) = [0.35], Max-Change = 0.0729
Stage 2 = 39, LL = -8512.7, AR(0.50) = [0.32], Max-Change = 0.0498
Stage 2 = 40, LL = -8474.1, AR(0.50) = [0.36], Max-Change = 0.0840
Stage 2 = 41, LL = -8463.3, AR(0.50) = [0.37], Max-Change = 0.1203
Stage 2 = 42, LL = -8514.2, AR(0.50) = [0.39], Max-Change = 0.1159
Stage 2 = 43, LL = -8526.4, AR(0.50) = [0.33], Max-Change = 0.0843
Stage 2 = 44, LL = -8519.8, AR(0.50) = [0.36], Max-Change = 0.1202
Stage 2 = 45, LL = -8494.0, AR(0.50) = [0.35], Max-Change = 0.0935
Stage 2 = 46, LL = -8488.0, AR(0.50) = [0.34], Max-Change = 0.0902
Stage 2 = 47, LL = -8466.1, AR(0.50) = [0.37], Max-Change = 0.0500
Stage 2 = 48, LL = -8510.5, AR(0.50) = [0.37], Max-Change = 0.1150
Stage 2 = 49, LL = -8513.6, AR(0.50) = [0.36], Max-Change = 0.0900
Stage 2 = 50, LL = -8511.8, AR(0.50) = [0.34], Max-Change = 0.1192
Stage 2 = 51, LL = -8467.9, AR(0.50) = [0.33], Max-Change = 0.0969
Stage 2 = 52, LL = -8495.3, AR(0.50) = [0.36], Max-Change = 0.0590
Stage 2 = 53, LL = -8477.4, AR(0.50) = [0.34], Max-Change = 0.0428
Stage 2 = 54, LL = -8510.4, AR(0.50) = [0.35], Max-Change = 0.1120
Stage 2 = 55, LL = -8507.1, AR(0.50) = [0.36], Max-Change = 0.1109
Stage 2 = 56, LL = -8469.3, AR(0.50) = [0.34], Max-Change = 0.1010
Stage 2 = 57, LL = -8502.3, AR(0.50) = [0.35], Max-Change = 0.0882
Stage 2 = 58, LL = -8496.4, AR(0.50) = [0.38], Max-Change = 0.1155
Stage 2 = 59, LL = -8535.6, AR(0.50) = [0.36], Max-Change = 0.0770
Stage 2 = 60, LL = -8563.1, AR(0.50) = [0.36], Max-Change = 0.1739
Stage 2 = 61, LL = -8517.2, AR(0.50) = [0.37], Max-Change = 0.0808
Stage 2 = 62, LL = -8469.8, AR(0.50) = [0.35], Max-Change = 0.1269
Stage 2 = 63, LL = -8513.1, AR(0.50) = [0.39], Max-Change = 0.0560
Stage 2 = 64, LL = -8477.2, AR(0.50) = [0.34], Max-Change = 0.0541
Stage 2 = 65, LL = -8494.4, AR(0.50) = [0.33], Max-Change = 0.0499
Stage 2 = 66, LL = -8463.1, AR(0.50) = [0.35], Max-Change = 0.1119
Stage 2 = 67, LL = -8474.8, AR(0.50) = [0.34], Max-Change = 0.1021
Stage 2 = 68, LL = -8470.3, AR(0.50) = [0.31], Max-Change = 0.0827
Stage 2 = 69, LL = -8492.9, AR(0.50) = [0.36], Max-Change = 0.1436
Stage 2 = 70, LL = -8505.6, AR(0.50) = [0.33], Max-Change = 0.0805
Stage 2 = 71, LL = -8478.3, AR(0.50) = [0.34], Max-Change = 0.0669
Stage 2 = 72, LL = -8490.8, AR(0.50) = [0.36], Max-Change = 0.1407
Stage 2 = 73, LL = -8488.9, AR(0.50) = [0.34], Max-Change = 0.1166
Stage 2 = 74, LL = -8429.4, AR(0.50) = [0.34], Max-Change = 0.1398
Stage 2 = 75, LL = -8467.9, AR(0.50) = [0.32], Max-Change = 0.1055
Stage 2 = 76, LL = -8434.2, AR(0.50) = [0.36], Max-Change = 0.0976
Stage 2 = 77, LL = -8455.1, AR(0.50) = [0.37], Max-Change = 0.1274
Stage 2 = 78, LL = -8477.6, AR(0.50) = [0.32], Max-Change = 0.0703
Stage 2 = 79, LL = -8451.3, AR(0.50) = [0.32], Max-Change = 0.0881
Stage 2 = 80, LL = -8458.2, AR(0.50) = [0.32], Max-Change = 0.0623
Stage 2 = 81, LL = -8474.5, AR(0.50) = [0.34], Max-Change = 0.1157
Stage 2 = 82, LL = -8480.7, AR(0.50) = [0.41], Max-Change = 0.0895
Stage 2 = 83, LL = -8474.9, AR(0.50) = [0.34], Max-Change = 0.1580
Stage 2 = 84, LL = -8481.6, AR(0.50) = [0.35], Max-Change = 0.0867
Stage 2 = 85, LL = -8453.9, AR(0.50) = [0.32], Max-Change = 0.0886
Stage 2 = 86, LL = -8469.6, AR(0.50) = [0.33], Max-Change = 0.0958
Stage 2 = 87, LL = -8460.7, AR(0.50) = [0.35], Max-Change = 0.1368
Stage 2 = 88, LL = -8459.6, AR(0.50) = [0.35], Max-Change = 0.0531
Stage 2 = 89, LL = -8509.8, AR(0.50) = [0.33], Max-Change = 0.1897
Stage 2 = 90, LL = -8487.4, AR(0.50) = [0.34], Max-Change = 0.0703
Stage 2 = 91, LL = -8516.1, AR(0.50) = [0.33], Max-Change = 0.0842
Stage 2 = 92, LL = -8501.1, AR(0.50) = [0.36], Max-Change = 0.0690
Stage 2 = 93, LL = -8480.1, AR(0.50) = [0.32], Max-Change = 0.0977
Stage 2 = 94, LL = -8486.3, AR(0.50) = [0.33], Max-Change = 0.1086
Stage 2 = 95, LL = -8455.4, AR(0.50) = [0.36], Max-Change = 0.0476
Stage 2 = 96, LL = -8455.4, AR(0.50) = [0.36], Max-Change = 0.0499
Stage 2 = 97, LL = -8461.7, AR(0.50) = [0.33], Max-Change = 0.0832
Stage 2 = 98, LL = -8426.9, AR(0.50) = [0.35], Max-Change = 0.2000
Stage 2 = 99, LL = -8449.3, AR(0.50) = [0.32], Max-Change = 0.1030
Stage 2 = 100, LL = -8456.7, AR(0.50) = [0.33], Max-Change = 0.0640
Stage 3 = 1, LL = -8485.2, AR(0.50) = [0.37], gam = 0.0000, Max-Change = 0.0000
Stage 3 = 2, LL = -8492.4, AR(0.50) = [0.36], gam = 0.1778, Max-Change = 0.0823
Stage 3 = 3, LL = -8518.6, AR(0.50) = [0.36], gam = 0.1057, Max-Change = 0.0431
Stage 3 = 4, LL = -8520.2, AR(0.50) = [0.40], gam = 0.0780, Max-Change = 0.0301
Stage 3 = 5, LL = -8496.3, AR(0.50) = [0.37], gam = 0.0629, Max-Change = 0.0267
Stage 3 = 6, LL = -8481.7, AR(0.50) = [0.34], gam = 0.0532, Max-Change = 0.0259
Stage 3 = 7, LL = -8465.5, AR(0.50) = [0.36], gam = 0.0464, Max-Change = 0.0170
Stage 3 = 8, LL = -8462.1, AR(0.50) = [0.34], gam = 0.0413, Max-Change = 0.0270
Stage 3 = 9, LL = -8484.7, AR(0.50) = [0.36], gam = 0.0374, Max-Change = 0.0201
Stage 3 = 10, LL = -8508.1, AR(0.50) = [0.33], gam = 0.0342, Max-Change = 0.0106
Stage 3 = 11, LL = -8494.5, AR(0.50) = [0.38], gam = 0.0316, Max-Change = 0.0109
Stage 3 = 12, LL = -8498.7, AR(0.50) = [0.34], gam = 0.0294, Max-Change = 0.0157
Stage 3 = 13, LL = -8490.6, AR(0.50) = [0.34], gam = 0.0276, Max-Change = 0.0129
Stage 3 = 14, LL = -8429.9, AR(0.50) = [0.36], gam = 0.0260, Max-Change = 0.0136
Stage 3 = 15, LL = -8489.7, AR(0.50) = [0.38], gam = 0.0246, Max-Change = 0.0178
Stage 3 = 16, LL = -8483.8, AR(0.50) = [0.31], gam = 0.0233, Max-Change = 0.0106
Stage 3 = 17, LL = -8484.4, AR(0.50) = [0.34], gam = 0.0222, Max-Change = 0.0230
Stage 3 = 18, LL = -8480.4, AR(0.50) = [0.34], gam = 0.0212, Max-Change = 0.0178
Stage 3 = 19, LL = -8475.8, AR(0.50) = [0.36], gam = 0.0203, Max-Change = 0.0069
Stage 3 = 20, LL = -8526.9, AR(0.50) = [0.33], gam = 0.0195, Max-Change = 0.0055
Stage 3 = 21, LL = -8531.3, AR(0.50) = [0.38], gam = 0.0188, Max-Change = 0.0071
Stage 3 = 22, LL = -8560.6, AR(0.50) = [0.35], gam = 0.0181, Max-Change = 0.0069
Stage 3 = 23, LL = -8529.1, AR(0.50) = [0.34], gam = 0.0175, Max-Change = 0.0092
Stage 3 = 24, LL = -8511.1, AR(0.50) = [0.33], gam = 0.0169, Max-Change = 0.0101
Stage 3 = 25, LL = -8509.2, AR(0.50) = [0.30], gam = 0.0164, Max-Change = 0.0058
Stage 3 = 26, LL = -8471.9, AR(0.50) = [0.34], gam = 0.0159, Max-Change = 0.0097
Stage 3 = 27, LL = -8467.5, AR(0.50) = [0.38], gam = 0.0154, Max-Change = 0.0063
Stage 3 = 28, LL = -8461.5, AR(0.50) = [0.37], gam = 0.0150, Max-Change = 0.0045
Stage 3 = 29, LL = -8453.2, AR(0.50) = [0.33], gam = 0.0146, Max-Change = 0.0031
Stage 3 = 30, LL = -8455.3, AR(0.50) = [0.36], gam = 0.0142, Max-Change = 0.0090
Stage 3 = 31, LL = -8472.4, AR(0.50) = [0.33], gam = 0.0139, Max-Change = 0.0087
Stage 3 = 32, LL = -8500.9, AR(0.50) = [0.33], gam = 0.0135, Max-Change = 0.0101
Stage 3 = 33, LL = -8495.4, AR(0.50) = [0.36], gam = 0.0132, Max-Change = 0.0070
Stage 3 = 34, LL = -8497.1, AR(0.50) = [0.36], gam = 0.0129, Max-Change = 0.0061
Stage 3 = 35, LL = -8510.7, AR(0.50) = [0.35], gam = 0.0126, Max-Change = 0.0060
Stage 3 = 36, LL = -8467.2, AR(0.50) = [0.35], gam = 0.0124, Max-Change = 0.0054
Stage 3 = 37, LL = -8494.2, AR(0.50) = [0.34], gam = 0.0121, Max-Change = 0.0060
Stage 3 = 38, LL = -8486.6, AR(0.50) = [0.35], gam = 0.0119, Max-Change = 0.0034
Stage 3 = 39, LL = -8488.7, AR(0.50) = [0.33], gam = 0.0116, Max-Change = 0.0037
Stage 3 = 40, LL = -8490.2, AR(0.50) = [0.33], gam = 0.0114, Max-Change = 0.0054
Stage 3 = 41, LL = -8489.5, AR(0.50) = [0.34], gam = 0.0112, Max-Change = 0.0057
Stage 3 = 42, LL = -8477.4, AR(0.50) = [0.37], gam = 0.0110, Max-Change = 0.0034
Stage 3 = 43, LL = -8495.2, AR(0.50) = [0.35], gam = 0.0108, Max-Change = 0.0047
Stage 3 = 44, LL = -8494.6, AR(0.50) = [0.38], gam = 0.0106, Max-Change = 0.0044
Stage 3 = 45, LL = -8505.5, AR(0.50) = [0.29], gam = 0.0104, Max-Change = 0.0048
Stage 3 = 46, LL = -8472.3, AR(0.50) = [0.35], gam = 0.0102, Max-Change = 0.0079
Stage 3 = 47, LL = -8474.1, AR(0.50) = [0.36], gam = 0.0101, Max-Change = 0.0041
Stage 3 = 48, LL = -8489.9, AR(0.50) = [0.37], gam = 0.0099, Max-Change = 0.0035
Stage 3 = 49, LL = -8496.5, AR(0.50) = [0.36], gam = 0.0098, Max-Change = 0.0037
Stage 3 = 50, LL = -8498.6, AR(0.50) = [0.35], gam = 0.0096, Max-Change = 0.0087
Stage 3 = 51, LL = -8463.0, AR(0.50) = [0.35], gam = 0.0095, Max-Change = 0.0057
Stage 3 = 52, LL = -8452.0, AR(0.50) = [0.34], gam = 0.0093, Max-Change = 0.0059
Stage 3 = 53, LL = -8478.1, AR(0.50) = [0.35], gam = 0.0092, Max-Change = 0.0037
Stage 3 = 54, LL = -8432.8, AR(0.50) = [0.35], gam = 0.0091, Max-Change = 0.0034
Stage 3 = 55, LL = -8478.4, AR(0.50) = [0.34], gam = 0.0089, Max-Change = 0.0043
Stage 3 = 56, LL = -8488.9, AR(0.50) = [0.39], gam = 0.0088, Max-Change = 0.0029
Stage 3 = 57, LL = -8490.9, AR(0.50) = [0.34], gam = 0.0087, Max-Change = 0.0031
Stage 3 = 58, LL = -8520.5, AR(0.50) = [0.34], gam = 0.0086, Max-Change = 0.0054
Stage 3 = 59, LL = -8489.6, AR(0.50) = [0.38], gam = 0.0085, Max-Change = 0.0026
Stage 3 = 60, LL = -8487.3, AR(0.50) = [0.31], gam = 0.0084, Max-Change = 0.0022
Stage 3 = 61, LL = -8475.6, AR(0.50) = [0.36], gam = 0.0082, Max-Change = 0.0046
Stage 3 = 62, LL = -8482.5, AR(0.50) = [0.34], gam = 0.0081, Max-Change = 0.0039
Stage 3 = 63, LL = -8494.9, AR(0.50) = [0.37], gam = 0.0080, Max-Change = 0.0025
Stage 3 = 64, LL = -8504.2, AR(0.50) = [0.33], gam = 0.0080, Max-Change = 0.0028
Stage 3 = 65, LL = -8500.9, AR(0.50) = [0.34], gam = 0.0079, Max-Change = 0.0047
Stage 3 = 66, LL = -8468.8, AR(0.50) = [0.36], gam = 0.0078, Max-Change = 0.0038
Stage 3 = 67, LL = -8466.4, AR(0.50) = [0.33], gam = 0.0077, Max-Change = 0.0024
Stage 3 = 68, LL = -8473.9, AR(0.50) = [0.34], gam = 0.0076, Max-Change = 0.0025
Stage 3 = 69, LL = -8515.0, AR(0.50) = [0.36], gam = 0.0075, Max-Change = 0.0024
Stage 3 = 70, LL = -8525.8, AR(0.50) = [0.40], gam = 0.0074, Max-Change = 0.0044
Stage 3 = 71, LL = -8502.5, AR(0.50) = [0.36], gam = 0.0073, Max-Change = 0.0038
Stage 3 = 72, LL = -8461.2, AR(0.50) = [0.38], gam = 0.0073, Max-Change = 0.0028
Stage 3 = 73, LL = -8474.9, AR(0.50) = [0.33], gam = 0.0072, Max-Change = 0.0057
Stage 3 = 74, LL = -8482.9, AR(0.50) = [0.36], gam = 0.0071, Max-Change = 0.0021
Stage 3 = 75, LL = -8518.3, AR(0.50) = [0.34], gam = 0.0070, Max-Change = 0.0047
Stage 3 = 76, LL = -8504.0, AR(0.50) = [0.31], gam = 0.0070, Max-Change = 0.0027
Stage 3 = 77, LL = -8498.1, AR(0.50) = [0.32], gam = 0.0069, Max-Change = 0.0026
Stage 3 = 78, LL = -8504.4, AR(0.50) = [0.33], gam = 0.0068, Max-Change = 0.0028
Stage 3 = 79, LL = -8475.1, AR(0.50) = [0.37], gam = 0.0068, Max-Change = 0.0030
Stage 3 = 80, LL = -8488.9, AR(0.50) = [0.36], gam = 0.0067, Max-Change = 0.0024
Stage 3 = 81, LL = -8501.0, AR(0.50) = [0.34], gam = 0.0066, Max-Change = 0.0035
Stage 3 = 82, LL = -8466.5, AR(0.50) = [0.37], gam = 0.0066, Max-Change = 0.0029
Stage 3 = 83, LL = -8495.1, AR(0.50) = [0.38], gam = 0.0065, Max-Change = 0.0029
Stage 3 = 84, LL = -8530.8, AR(0.50) = [0.31], gam = 0.0065, Max-Change = 0.0019
Stage 3 = 85, LL = -8518.6, AR(0.50) = [0.40], gam = 0.0064, Max-Change = 0.0046
Stage 3 = 86, LL = -8487.3, AR(0.50) = [0.35], gam = 0.0064, Max-Change = 0.0023
Stage 3 = 87, LL = -8516.2, AR(0.50) = [0.36], gam = 0.0063, Max-Change = 0.0033
Stage 3 = 88, LL = -8478.6, AR(0.50) = [0.36], gam = 0.0062, Max-Change = 0.0025
Stage 3 = 89, LL = -8486.6, AR(0.50) = [0.32], gam = 0.0062, Max-Change = 0.0050
Stage 3 = 90, LL = -8475.2, AR(0.50) = [0.33], gam = 0.0061, Max-Change = 0.0038
Stage 3 = 91, LL = -8457.6, AR(0.50) = [0.35], gam = 0.0061, Max-Change = 0.0021
Stage 3 = 92, LL = -8432.9, AR(0.50) = [0.34], gam = 0.0060, Max-Change = 0.0024
Stage 3 = 93, LL = -8445.7, AR(0.50) = [0.34], gam = 0.0060, Max-Change = 0.0020
Stage 3 = 94, LL = -8470.2, AR(0.50) = [0.36], gam = 0.0059, Max-Change = 0.0018
Stage 3 = 95, LL = -8495.0, AR(0.50) = [0.34], gam = 0.0059, Max-Change = 0.0027
Stage 3 = 96, LL = -8476.7, AR(0.50) = [0.35], gam = 0.0058, Max-Change = 0.0034
Stage 3 = 97, LL = -8494.1, AR(0.50) = [0.35], gam = 0.0058, Max-Change = 0.0033
Stage 3 = 98, LL = -8479.5, AR(0.50) = [0.36], gam = 0.0058, Max-Change = 0.0034
Stage 3 = 99, LL = -8471.6, AR(0.50) = [0.30], gam = 0.0057, Max-Change = 0.0025
Stage 3 = 100, LL = -8507.1, AR(0.50) = [0.36], gam = 0.0057, Max-Change = 0.0027
Stage 3 = 101, LL = -8492.9, AR(0.50) = [0.37], gam = 0.0056, Max-Change = 0.0023
Stage 3 = 102, LL = -8514.0, AR(0.50) = [0.37], gam = 0.0056, Max-Change = 0.0030
Stage 3 = 103, LL = -8502.3, AR(0.50) = [0.35], gam = 0.0055, Max-Change = 0.0025
Stage 3 = 104, LL = -8505.0, AR(0.50) = [0.35], gam = 0.0055, Max-Change = 0.0022
Stage 3 = 105, LL = -8544.3, AR(0.50) = [0.38], gam = 0.0055, Max-Change = 0.0050
Stage 3 = 106, LL = -8508.4, AR(0.50) = [0.36], gam = 0.0054, Max-Change = 0.0055
Stage 3 = 107, LL = -8475.8, AR(0.50) = [0.35], gam = 0.0054, Max-Change = 0.0034
Stage 3 = 108, LL = -8489.5, AR(0.50) = [0.38], gam = 0.0053, Max-Change = 0.0015
Stage 3 = 109, LL = -8483.7, AR(0.50) = [0.33], gam = 0.0053, Max-Change = 0.0029
Stage 3 = 110, LL = -8471.5, AR(0.50) = [0.35], gam = 0.0053, Max-Change = 0.0029
Stage 3 = 111, LL = -8465.9, AR(0.50) = [0.33], gam = 0.0052, Max-Change = 0.0013
Stage 3 = 112, LL = -8493.5, AR(0.50) = [0.34], gam = 0.0052, Max-Change = 0.0023
Stage 3 = 113, LL = -8487.3, AR(0.50) = [0.34], gam = 0.0052, Max-Change = 0.0019
Stage 3 = 114, LL = -8490.0, AR(0.50) = [0.36], gam = 0.0051, Max-Change = 0.0020
Stage 3 = 115, LL = -8450.8, AR(0.50) = [0.33], gam = 0.0051, Max-Change = 0.0026
Stage 3 = 116, LL = -8434.0, AR(0.50) = [0.37], gam = 0.0051, Max-Change = 0.0021
Stage 3 = 117, LL = -8442.3, AR(0.50) = [0.29], gam = 0.0050, Max-Change = 0.0038
Stage 3 = 118, LL = -8472.5, AR(0.50) = [0.35], gam = 0.0050, Max-Change = 0.0016
Stage 3 = 119, LL = -8483.4, AR(0.50) = [0.34], gam = 0.0050, Max-Change = 0.0023
Stage 3 = 120, LL = -8503.5, AR(0.50) = [0.36], gam = 0.0049, Max-Change = 0.0025
Stage 3 = 121, LL = -8505.5, AR(0.50) = [0.37], gam = 0.0049, Max-Change = 0.0036
Stage 3 = 122, LL = -8496.0, AR(0.50) = [0.32], gam = 0.0049, Max-Change = 0.0017
Stage 3 = 123, LL = -8495.0, AR(0.50) = [0.38], gam = 0.0048, Max-Change = 0.0013
Stage 3 = 124, LL = -8470.9, AR(0.50) = [0.35], gam = 0.0048, Max-Change = 0.0024
Stage 3 = 125, LL = -8526.2, AR(0.50) = [0.32], gam = 0.0048, Max-Change = 0.0014
Stage 3 = 126, LL = -8510.5, AR(0.50) = [0.36], gam = 0.0048, Max-Change = 0.0019
Stage 3 = 127, LL = -8485.2, AR(0.50) = [0.37], gam = 0.0047, Max-Change = 0.0055
Stage 3 = 128, LL = -8489.5, AR(0.50) = [0.32], gam = 0.0047, Max-Change = 0.0054
Stage 3 = 129, LL = -8525.1, AR(0.50) = [0.33], gam = 0.0047, Max-Change = 0.0041
Stage 3 = 130, LL = -8495.2, AR(0.50) = [0.38], gam = 0.0046, Max-Change = 0.0026
Stage 3 = 131, LL = -8519.5, AR(0.50) = [0.36], gam = 0.0046, Max-Change = 0.0026
Stage 3 = 132, LL = -8492.5, AR(0.50) = [0.36], gam = 0.0046, Max-Change = 0.0024
Stage 3 = 133, LL = -8521.0, AR(0.50) = [0.37], gam = 0.0046, Max-Change = 0.0013
Stage 3 = 134, LL = -8515.4, AR(0.50) = [0.38], gam = 0.0045, Max-Change = 0.0020
Stage 3 = 135, LL = -8488.2, AR(0.50) = [0.37], gam = 0.0045, Max-Change = 0.0019
Stage 3 = 136, LL = -8486.0, AR(0.50) = [0.38], gam = 0.0045, Max-Change = 0.0016
Stage 3 = 137, LL = -8476.5, AR(0.50) = [0.40], gam = 0.0045, Max-Change = 0.0017
Stage 3 = 138, LL = -8482.9, AR(0.50) = [0.37], gam = 0.0044, Max-Change = 0.0015
Stage 3 = 139, LL = -8454.4, AR(0.50) = [0.35], gam = 0.0044, Max-Change = 0.0020
Stage 3 = 140, LL = -8464.3, AR(0.50) = [0.37], gam = 0.0044, Max-Change = 0.0022
Stage 3 = 141, LL = -8474.3, AR(0.50) = [0.38], gam = 0.0044, Max-Change = 0.0025
Stage 3 = 142, LL = -8498.4, AR(0.50) = [0.37], gam = 0.0043, Max-Change = 0.0022
Stage 3 = 143, LL = -8467.1, AR(0.50) = [0.33], gam = 0.0043, Max-Change = 0.0021
Stage 3 = 144, LL = -8454.2, AR(0.50) = [0.34], gam = 0.0043, Max-Change = 0.0014
Stage 3 = 145, LL = -8474.6, AR(0.50) = [0.37], gam = 0.0043, Max-Change = 0.0012
Stage 3 = 146, LL = -8481.2, AR(0.50) = [0.36], gam = 0.0043, Max-Change = 0.0012
Stage 3 = 147, LL = -8423.8, AR(0.50) = [0.34], gam = 0.0042, Max-Change = 0.0027
Stage 3 = 148, LL = -8433.9, AR(0.50) = [0.32], gam = 0.0042, Max-Change = 0.0021
Stage 3 = 149, LL = -8468.0, AR(0.50) = [0.36], gam = 0.0042, Max-Change = 0.0028
Stage 3 = 150, LL = -8459.9, AR(0.50) = [0.33], gam = 0.0042, Max-Change = 0.0020
Stage 3 = 151, LL = -8483.9, AR(0.50) = [0.35], gam = 0.0041, Max-Change = 0.0028
Stage 3 = 152, LL = -8508.3, AR(0.50) = [0.37], gam = 0.0041, Max-Change = 0.0014
Stage 3 = 153, LL = -8466.0, AR(0.50) = [0.34], gam = 0.0041, Max-Change = 0.0020
Stage 3 = 154, LL = -8476.5, AR(0.50) = [0.36], gam = 0.0041, Max-Change = 0.0025
Stage 3 = 155, LL = -8499.9, AR(0.50) = [0.39], gam = 0.0041, Max-Change = 0.0017
Stage 3 = 156, LL = -8517.1, AR(0.50) = [0.31], gam = 0.0040, Max-Change = 0.0020
Stage 3 = 157, LL = -8509.3, AR(0.50) = [0.35], gam = 0.0040, Max-Change = 0.0012
Stage 3 = 158, LL = -8499.2, AR(0.50) = [0.34], gam = 0.0040, Max-Change = 0.0018
Stage 3 = 159, LL = -8478.4, AR(0.50) = [0.37], gam = 0.0040, Max-Change = 0.0018
Stage 3 = 160, LL = -8514.6, AR(0.50) = [0.38], gam = 0.0040, Max-Change = 0.0012
Stage 3 = 161, LL = -8481.1, AR(0.50) = [0.37], gam = 0.0040, Max-Change = 0.0015
Stage 3 = 162, LL = -8469.7, AR(0.50) = [0.34], gam = 0.0039, Max-Change = 0.0030
Stage 3 = 163, LL = -8509.5, AR(0.50) = [0.35], gam = 0.0039, Max-Change = 0.0015
Stage 3 = 164, LL = -8499.2, AR(0.50) = [0.34], gam = 0.0039, Max-Change = 0.0012
Stage 3 = 165, LL = -8470.3, AR(0.50) = [0.31], gam = 0.0039, Max-Change = 0.0026
Stage 3 = 166, LL = -8486.7, AR(0.50) = [0.38], gam = 0.0039, Max-Change = 0.0025
Stage 3 = 167, LL = -8498.0, AR(0.50) = [0.36], gam = 0.0038, Max-Change = 0.0023
Stage 3 = 168, LL = -8485.3, AR(0.50) = [0.33], gam = 0.0038, Max-Change = 0.0014
Stage 3 = 169, LL = -8497.6, AR(0.50) = [0.35], gam = 0.0038, Max-Change = 0.0022
Stage 3 = 170, LL = -8492.9, AR(0.50) = [0.33], gam = 0.0038, Max-Change = 0.0011
Stage 3 = 171, LL = -8469.2, AR(0.50) = [0.38], gam = 0.0038, Max-Change = 0.0013
Stage 3 = 172, LL = -8536.9, AR(0.50) = [0.35], gam = 0.0038, Max-Change = 0.0024
Stage 3 = 173, LL = -8513.1, AR(0.50) = [0.41], gam = 0.0037, Max-Change = 0.0026
Stage 3 = 174, LL = -8514.8, AR(0.50) = [0.36], gam = 0.0037, Max-Change = 0.0024
Stage 3 = 175, LL = -8484.1, AR(0.50) = [0.35], gam = 0.0037, Max-Change = 0.0021
Stage 3 = 176, LL = -8508.2, AR(0.50) = [0.36], gam = 0.0037, Max-Change = 0.0021
Stage 3 = 177, LL = -8453.5, AR(0.50) = [0.33], gam = 0.0037, Max-Change = 0.0016
Stage 3 = 178, LL = -8460.5, AR(0.50) = [0.36], gam = 0.0037, Max-Change = 0.0021
Stage 3 = 179, LL = -8523.7, AR(0.50) = [0.32], gam = 0.0036, Max-Change = 0.0040
Stage 3 = 180, LL = -8477.5, AR(0.50) = [0.37], gam = 0.0036, Max-Change = 0.0018
Stage 3 = 181, LL = -8451.3, AR(0.50) = [0.35], gam = 0.0036, Max-Change = 0.0012
Stage 3 = 182, LL = -8497.3, AR(0.50) = [0.36], gam = 0.0036, Max-Change = 0.0015
Stage 3 = 183, LL = -8531.2, AR(0.50) = [0.34], gam = 0.0036, Max-Change = 0.0027
Stage 3 = 184, LL = -8499.0, AR(0.50) = [0.36], gam = 0.0036, Max-Change = 0.0015
Stage 3 = 185, LL = -8481.9, AR(0.50) = [0.35], gam = 0.0036, Max-Change = 0.0009
Stage 3 = 186, LL = -8526.6, AR(0.50) = [0.39], gam = 0.0035, Max-Change = 0.0016
Stage 3 = 187, LL = -8484.6, AR(0.50) = [0.35], gam = 0.0035, Max-Change = 0.0022
Stage 3 = 188, LL = -8510.3, AR(0.50) = [0.35], gam = 0.0035, Max-Change = 0.0026
Stage 3 = 189, LL = -8512.1, AR(0.50) = [0.33], gam = 0.0035, Max-Change = 0.0012
Stage 3 = 190, LL = -8504.3, AR(0.50) = [0.33], gam = 0.0035, Max-Change = 0.0015
Stage 3 = 191, LL = -8486.6, AR(0.50) = [0.35], gam = 0.0035, Max-Change = 0.0019
Stage 3 = 192, LL = -8557.6, AR(0.50) = [0.39], gam = 0.0035, Max-Change = 0.0026
Stage 3 = 193, LL = -8476.0, AR(0.50) = [0.40], gam = 0.0034, Max-Change = 0.0013
Stage 3 = 194, LL = -8522.3, AR(0.50) = [0.36], gam = 0.0034, Max-Change = 0.0013
Stage 3 = 195, LL = -8503.9, AR(0.50) = [0.32], gam = 0.0034, Max-Change = 0.0012
Stage 3 = 196, LL = -8504.0, AR(0.50) = [0.36], gam = 0.0034, Max-Change = 0.0026
Stage 3 = 197, LL = -8489.0, AR(0.50) = [0.36], gam = 0.0034, Max-Change = 0.0010
Stage 3 = 198, LL = -8467.2, AR(0.50) = [0.34], gam = 0.0034, Max-Change = 0.0008
Stage 3 = 199, LL = -8461.8, AR(0.50) = [0.33], gam = 0.0034, Max-Change = 0.0024
Stage 3 = 200, LL = -8473.0, AR(0.50) = [0.36], gam = 0.0034, Max-Change = 0.0021
Stage 3 = 201, LL = -8508.0, AR(0.50) = [0.35], gam = 0.0033, Max-Change = 0.0020
Stage 3 = 202, LL = -8515.5, AR(0.50) = [0.36], gam = 0.0033, Max-Change = 0.0009
Stage 3 = 203, LL = -8501.8, AR(0.50) = [0.35], gam = 0.0033, Max-Change = 0.0013
Stage 3 = 204, LL = -8515.7, AR(0.50) = [0.33], gam = 0.0033, Max-Change = 0.0010
Stage 3 = 205, LL = -8507.9, AR(0.50) = [0.36], gam = 0.0033, Max-Change = 0.0029
Stage 3 = 206, LL = -8494.9, AR(0.50) = [0.33], gam = 0.0033, Max-Change = 0.0016
Stage 3 = 207, LL = -8493.1, AR(0.50) = [0.34], gam = 0.0033, Max-Change = 0.0011
Stage 3 = 208, LL = -8482.5, AR(0.50) = [0.31], gam = 0.0033, Max-Change = 0.0010
Stage 3 = 209, LL = -8472.4, AR(0.50) = [0.35], gam = 0.0032, Max-Change = 0.0010
Stage 3 = 210, LL = -8477.8, AR(0.50) = [0.33], gam = 0.0032, Max-Change = 0.0012
Stage 3 = 211, LL = -8481.3, AR(0.50) = [0.32], gam = 0.0032, Max-Change = 0.0013
Stage 3 = 212, LL = -8481.6, AR(0.50) = [0.37], gam = 0.0032, Max-Change = 0.0011
Stage 3 = 213, LL = -8493.8, AR(0.50) = [0.34], gam = 0.0032, Max-Change = 0.0006
Stage 3 = 214, LL = -8446.4, AR(0.50) = [0.37], gam = 0.0032, Max-Change = 0.0012
Stage 3 = 215, LL = -8459.7, AR(0.50) = [0.33], gam = 0.0032, Max-Change = 0.0007
Stage 3 = 216, LL = -8486.9, AR(0.50) = [0.36], gam = 0.0032, Max-Change = 0.0012
Stage 3 = 217, LL = -8483.4, AR(0.50) = [0.31], gam = 0.0032, Max-Change = 0.0013
Stage 3 = 218, LL = -8467.8, AR(0.50) = [0.31], gam = 0.0031, Max-Change = 0.0013
Stage 3 = 219, LL = -8463.1, AR(0.50) = [0.40], gam = 0.0031, Max-Change = 0.0018
Stage 3 = 220, LL = -8531.8, AR(0.50) = [0.39], gam = 0.0031, Max-Change = 0.0011
Stage 3 = 221, LL = -8514.0, AR(0.50) = [0.34], gam = 0.0031, Max-Change = 0.0011
Stage 3 = 222, LL = -8503.4, AR(0.50) = [0.37], gam = 0.0031, Max-Change = 0.0012
Stage 3 = 223, LL = -8467.4, AR(0.50) = [0.35], gam = 0.0031, Max-Change = 0.0014
Stage 3 = 224, LL = -8498.0, AR(0.50) = [0.35], gam = 0.0031, Max-Change = 0.0018
Stage 3 = 225, LL = -8479.5, AR(0.50) = [0.35], gam = 0.0031, Max-Change = 0.0010
Stage 3 = 226, LL = -8468.6, AR(0.50) = [0.34], gam = 0.0031, Max-Change = 0.0010
Stage 3 = 227, LL = -8507.5, AR(0.50) = [0.33], gam = 0.0031, Max-Change = 0.0019
Stage 3 = 228, LL = -8493.2, AR(0.50) = [0.37], gam = 0.0030, Max-Change = 0.0013
Stage 3 = 229, LL = -8458.2, AR(0.50) = [0.34], gam = 0.0030, Max-Change = 0.0011
Stage 3 = 230, LL = -8527.2, AR(0.50) = [0.34], gam = 0.0030, Max-Change = 0.0032
Stage 3 = 231, LL = -8514.0, AR(0.50) = [0.37], gam = 0.0030, Max-Change = 0.0013
Stage 3 = 232, LL = -8463.1, AR(0.50) = [0.41], gam = 0.0030, Max-Change = 0.0012
Stage 3 = 233, LL = -8468.5, AR(0.50) = [0.40], gam = 0.0030, Max-Change = 0.0011
Stage 3 = 234, LL = -8467.1, AR(0.50) = [0.36], gam = 0.0030, Max-Change = 0.0010
Stage 3 = 235, LL = -8490.2, AR(0.50) = [0.32], gam = 0.0030, Max-Change = 0.0011
Stage 3 = 236, LL = -8471.9, AR(0.50) = [0.36], gam = 0.0030, Max-Change = 0.0013
Stage 3 = 237, LL = -8464.7, AR(0.50) = [0.34], gam = 0.0030, Max-Change = 0.0013
Stage 3 = 238, LL = -8477.8, AR(0.50) = [0.36], gam = 0.0029, Max-Change = 0.0014
Stage 3 = 239, LL = -8478.9, AR(0.50) = [0.37], gam = 0.0029, Max-Change = 0.0023
Stage 3 = 240, LL = -8503.2, AR(0.50) = [0.37], gam = 0.0029, Max-Change = 0.0013
Stage 3 = 241, LL = -8500.5, AR(0.50) = [0.37], gam = 0.0029, Max-Change = 0.0018
Stage 3 = 242, LL = -8470.6, AR(0.50) = [0.38], gam = 0.0029, Max-Change = 0.0018
Stage 3 = 243, LL = -8471.8, AR(0.50) = [0.38], gam = 0.0029, Max-Change = 0.0016
Stage 3 = 244, LL = -8499.4, AR(0.50) = [0.35], gam = 0.0029, Max-Change = 0.0018
Stage 3 = 245, LL = -8495.4, AR(0.50) = [0.37], gam = 0.0029, Max-Change = 0.0008
Stage 3 = 246, LL = -8467.7, AR(0.50) = [0.36], gam = 0.0029, Max-Change = 0.0011
Stage 3 = 247, LL = -8489.6, AR(0.50) = [0.35], gam = 0.0029, Max-Change = 0.0012
Stage 3 = 248, LL = -8468.6, AR(0.50) = [0.35], gam = 0.0029, Max-Change = 0.0012
Stage 3 = 249, LL = -8462.9, AR(0.50) = [0.35], gam = 0.0028, Max-Change = 0.0011
Stage 3 = 250, LL = -8517.7, AR(0.50) = [0.35], gam = 0.0028, Max-Change = 0.0017
Stage 3 = 251, LL = -8503.7, AR(0.50) = [0.31], gam = 0.0028, Max-Change = 0.0014
Stage 3 = 252, LL = -8510.2, AR(0.50) = [0.34], gam = 0.0028, Max-Change = 0.0014
Stage 3 = 253, LL = -8503.4, AR(0.50) = [0.36], gam = 0.0028, Max-Change = 0.0012
Stage 3 = 254, LL = -8476.3, AR(0.50) = [0.33], gam = 0.0028, Max-Change = 0.0008
Stage 3 = 255, LL = -8459.2, AR(0.50) = [0.39], gam = 0.0028, Max-Change = 0.0024
Stage 3 = 256, LL = -8471.8, AR(0.50) = [0.34], gam = 0.0028, Max-Change = 0.0007
Stage 3 = 257, LL = -8453.9, AR(0.50) = [0.36], gam = 0.0028, Max-Change = 0.0011
Stage 3 = 258, LL = -8474.6, AR(0.50) = [0.35], gam = 0.0028, Max-Change = 0.0013
Stage 3 = 259, LL = -8470.0, AR(0.50) = [0.34], gam = 0.0028, Max-Change = 0.0019
Stage 3 = 260, LL = -8473.9, AR(0.50) = [0.33], gam = 0.0028, Max-Change = 0.0010
Stage 3 = 261, LL = -8497.4, AR(0.50) = [0.32], gam = 0.0027, Max-Change = 0.0016
Stage 3 = 262, LL = -8503.4, AR(0.50) = [0.34], gam = 0.0027, Max-Change = 0.0018
Stage 3 = 263, LL = -8486.7, AR(0.50) = [0.34], gam = 0.0027, Max-Change = 0.0013
Stage 3 = 264, LL = -8510.4, AR(0.50) = [0.38], gam = 0.0027, Max-Change = 0.0009
Stage 3 = 265, LL = -8477.7, AR(0.50) = [0.34], gam = 0.0027, Max-Change = 0.0011
Stage 3 = 266, LL = -8495.4, AR(0.50) = [0.37], gam = 0.0027, Max-Change = 0.0009
Stage 3 = 267, LL = -8513.1, AR(0.50) = [0.35], gam = 0.0027, Max-Change = 0.0010
Stage 3 = 268, LL = -8465.5, AR(0.50) = [0.37], gam = 0.0027, Max-Change = 0.0020
Stage 3 = 269, LL = -8468.4, AR(0.50) = [0.35], gam = 0.0027, Max-Change = 0.0015
Stage 3 = 270, LL = -8496.7, AR(0.50) = [0.34], gam = 0.0027, Max-Change = 0.0026
Stage 3 = 271, LL = -8512.2, AR(0.50) = [0.32], gam = 0.0027, Max-Change = 0.0016
Stage 3 = 272, LL = -8488.1, AR(0.50) = [0.35], gam = 0.0027, Max-Change = 0.0010
Stage 3 = 273, LL = -8478.7, AR(0.50) = [0.32], gam = 0.0027, Max-Change = 0.0007
Stage 3 = 274, LL = -8455.8, AR(0.50) = [0.35], gam = 0.0026, Max-Change = 0.0009
Calculating log-likelihood...3 Descriptive results
3.1 Participants
Page 2. Therefore, a total of 500 children were randomly selected for the analyses. The randomness processwas initiated in the fairsubset R package,17 with the seed defined at 15 and RNGversion set at 3.6. This subsample comprised 276 males (55.2%) and 224 females (44.8%).
ds_60_random %>% Warning messages: 1: In grepl(“”, x, fixed = TRUE) : input string 1 is invalid UTF-8 2: In grepl(“”, x, fixed = TRUE) : input string 1 is invalid UTF-8
mutate(sex = factor(sex)) %>%
tableby(~ sex, data = .) %>% summary()| Overall (N=500) | |
|---|---|
| sex | |
| 1 | 276 (55.2%) |
| 2 | 224 (44.8%) |
NA
3.2 Mean score
Page 3. The mean score for these participants was 41 (standard deviation = 6.4, range: 0–205).
ds_60_random %>% Warning messages: 1: In grepl(“”, x, fixed = TRUE) : input string 1 is invalid UTF-8 2: In grepl(“”, x, fixed = TRUE) : input string 1 is invalid UTF-8
tableby(~ score, data = .) %>% summary()| Overall (N=500) | |
|---|---|
| score | |
| Mean (SD) | 41.000 (36.400) |
| Range | 0.000 - 205.000 |
NA
Page 3. No difference was found between this score and the score that was obtained with the full data set (t 22829 = -0.982, p = 0.326).
t.test(ds_60$score, ds_60_random$score, var.equal = T)
Two Sample t-test
data: ds_60$score and ds_60_random$score
t = -0.98204, df = 22829, p-value = 0.3261
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-4.551496 1.513030
sample estimates:
mean of x mean of y
39.48077 41.00000 3.3 ASQ Items
ds_60_random %>% select(starts_with("q")) %>%
mutate_all(., ~as.factor(.)) %>%
tableby(~., data = .) %>% summary()| Overall (N=500) | |
|---|---|
| q_1 | |
| 0 | 417 (83.4%) |
| 5 | 77 (15.4%) |
| 10 | 6 (1.2%) |
| q_2 | |
| 0 | 326 (65.2%) |
| 5 | 110 (22.0%) |
| 10 | 64 (12.8%) |
| q_3 | |
| 0 | 355 (71.0%) |
| 5 | 127 (25.4%) |
| 10 | 18 (3.6%) |
| q_4 | |
| 0 | 391 (78.2%) |
| 5 | 82 (16.4%) |
| 10 | 27 (5.4%) |
| q_5 | |
| 0 | 412 (82.4%) |
| 5 | 66 (13.2%) |
| 10 | 22 (4.4%) |
| q_6 | |
| 0 | 387 (77.4%) |
| 5 | 63 (12.6%) |
| 10 | 50 (10.0%) |
| q_7 | |
| 0 | 370 (74.0%) |
| 5 | 101 (20.2%) |
| 10 | 29 (5.8%) |
| q_8 | |
| 0 | 447 (89.4%) |
| 5 | 42 (8.4%) |
| 10 | 11 (2.2%) |
| q_9 | |
| 0 | 380 (76.0%) |
| 5 | 76 (15.2%) |
| 10 | 44 (8.8%) |
| q_10 | |
| 0 | 451 (90.2%) |
| 5 | 47 (9.4%) |
| 10 | 2 (0.4%) |
| q_11 | |
| 0 | 483 (96.6%) |
| 5 | 8 (1.6%) |
| 10 | 9 (1.8%) |
| q_12 | |
| 0 | 461 (92.2%) |
| 5 | 18 (3.6%) |
| 10 | 21 (4.2%) |
| q_13 | |
| 0 | 403 (80.6%) |
| 5 | 84 (16.8%) |
| 10 | 13 (2.6%) |
| q_14 | |
| 0 | 309 (61.8%) |
| 5 | 172 (34.4%) |
| 10 | 19 (3.8%) |
| q_15 | |
| 0 | 357 (71.4%) |
| 5 | 128 (25.6%) |
| 10 | 15 (3.0%) |
| q_16 | |
| 0 | 298 (59.6%) |
| 5 | 112 (22.4%) |
| 10 | 90 (18.0%) |
| q_17 | |
| 0 | 425 (85.0%) |
| 5 | 65 (13.0%) |
| 10 | 10 (2.0%) |
| q_18 | |
| 0 | 454 (90.8%) |
| 5 | 37 (7.4%) |
| 10 | 9 (1.8%) |
| q_19 | |
| 0 | 388 (77.6%) |
| 5 | 89 (17.8%) |
| 10 | 23 (4.6%) |
| q_20 | |
| 0 | 382 (76.4%) |
| 5 | 93 (18.6%) |
| 10 | 25 (5.0%) |
| q_21 | |
| 0 | 380 (76.0%) |
| 5 | 90 (18.0%) |
| 10 | 30 (6.0%) |
| q_22 | |
| 0 | 465 (93.0%) |
| 5 | 16 (3.2%) |
| 10 | 19 (3.8%) |
| q_23 | |
| 0 | 483 (96.6%) |
| 5 | 10 (2.0%) |
| 10 | 7 (1.4%) |
| q_24 | |
| 0 | 324 (64.8%) |
| 5 | 146 (29.2%) |
| 10 | 30 (6.0%) |
| q_25 | |
| 0 | 417 (83.4%) |
| 5 | 57 (11.4%) |
| 10 | 26 (5.2%) |
| q_26 | |
| 0 | 393 (78.6%) |
| 5 | 75 (15.0%) |
| 10 | 32 (6.4%) |
| q_27 | |
| 0 | 305 (61.0%) |
| 5 | 154 (30.8%) |
| 10 | 41 (8.2%) |
| q_28 | |
| 0 | 452 (90.4%) |
| 5 | 43 (8.6%) |
| 10 | 5 (1.0%) |
| q_29 | |
| 0 | 470 (94.0%) |
| 5 | 24 (4.8%) |
| 10 | 6 (1.2%) |
| q_30 | |
| 0 | 395 (79.0%) |
| 5 | 77 (15.4%) |
| 10 | 28 (5.6%) |
| q_31 | |
| 0 | 297 (59.4%) |
| 5 | 173 (34.6%) |
| 10 | 30 (6.0%) |
| q_32 | |
| 0 | 414 (82.8%) |
| 5 | 56 (11.2%) |
| 10 | 30 (6.0%) |
NA
4 Reliability
Page 3. Cronbach’s α for this interval was 0.86 (95% confidence interval [CI]: 0.85–0.88), with an average interitem correlation of 0.17 (95% CI: 0.15–0.19). This age interval is composed of 32 items, in which respondents choose one option that best aligns with a target behavior of the child.
ds_60_random %>% select(starts_with("q"))%>% alpha()
Reliability analysis
Call: alpha(x = .)
lower alpha upper 95% confidence boundaries
0.85 0.86 0.88
Reliability if an item is dropped:
Item statistics
Non missing response frequency for each item
0 5 10 miss
q_1 0.83 0.15 0.01 0
q_2 0.65 0.22 0.13 0
q_3 0.71 0.25 0.04 0
q_4 0.78 0.16 0.05 0
q_5 0.82 0.13 0.04 0
q_6 0.77 0.13 0.10 0
q_7 0.74 0.20 0.06 0
q_8 0.89 0.08 0.02 0
q_9 0.76 0.15 0.09 0
q_10 0.90 0.09 0.00 0
q_11 0.97 0.02 0.02 0
q_12 0.92 0.04 0.04 0
q_13 0.81 0.17 0.03 0
q_14 0.62 0.34 0.04 0
q_15 0.71 0.26 0.03 0
q_16 0.60 0.22 0.18 0
q_17 0.85 0.13 0.02 0
q_18 0.91 0.07 0.02 0
q_19 0.78 0.18 0.05 0
q_20 0.76 0.19 0.05 0
q_21 0.76 0.18 0.06 0
q_22 0.93 0.03 0.04 0
q_23 0.97 0.02 0.01 0
q_24 0.65 0.29 0.06 0
q_25 0.83 0.11 0.05 0
q_26 0.79 0.15 0.06 0
q_27 0.61 0.31 0.08 0
q_28 0.90 0.09 0.01 0
q_29 0.94 0.05 0.01 0
q_30 0.79 0.15 0.06 0
q_31 0.59 0.35 0.06 0
q_32 0.83 0.11 0.06 05 Items
Page 4. The distribution of ASQ:SE items was right-skewed, indicating deviation fromnormality and that the items’meanswere greater than the medians. Skews ranged from 0.87 to 6.04. Kurtosis ranged from 0.81 to 37.29. The Kaiser–Meyer– Olkin test result was 0.86.
Page 9. First result
ds_60_random %>% select(starts_with("q")) %>%
mutate_all(., ~case_when(. == "0" ~ 1,
. == "5" ~ 2,
. == "10" ~ 3)) %>%
pivot_longer(everything()) %>%
ggplot(., aes(as.numeric(value), fill = name)) +
geom_density(alpha = 0.3)
6 Exploratory analysis
Page 4. The Kaiser–Meyer– Olkin test result was 0.86. The Bartlett test result was 4629.517 (df¼496, p<0.001).
6.1 KMO
ds_60_random %>% select(starts_with("q")) %>%
mutate_all(., ~case_when(. == "0" ~ 1,
. == "5" ~ 2,
. == "10" ~ 3)) %>% KMO()Kaiser-Meyer-Olkin factor adequacy
Call: KMO(r = .)
Overall MSA = 0.86
MSA for each item =
q_1 q_2 q_3 q_4 q_5 q_6 q_7 q_8 q_9 q_10 q_11 q_12 q_13 q_14 q_15 q_16 q_17 q_18 q_19 q_20 q_21 q_22 q_23 q_24 q_25 q_26 q_27 q_28 q_29 q_30
0.92 0.78 0.81 0.81 0.89 0.81 0.91 0.79 0.88 0.86 0.63 0.78 0.90 0.87 0.91 0.90 0.76 0.77 0.80 0.91 0.84 0.80 0.76 0.90 0.90 0.86 0.86 0.85 0.76 0.91
q_31 q_32
0.91 0.80 6.2 Bartlett
ds_60_random %>% select(starts_with("q")) %>%
mutate_all(., ~case_when(. == "0" ~ 1,
. == "5" ~ 2,
. == "10" ~ 3)) %>% psych::cortest.bartlett()R was not square, finding R from data$chisq
[1] 4629.517
$p.value
[1] 0
$df
[1] 4966.3 Decide how many factors will be retained
6.4 Polychoric matrix as input
rho_60 <- ds_60_random %>% select(starts_with("q")) %>%
mutate_all(., ~case_when(. == "0" ~ 1,
. == "5" ~ 2,
. == "10" ~ 3)) %>%
polychoric(.)
Warning in cor.smooth(mat) :
Matrix was not positive definite, smoothing was done6.5 Get rho from the polychoric matrix
rho_60 <- rho_60$rho 6.6 Parallel Analysis (polychoric)
The following parallel analysis will define an arbitrarily set of subjects
parallel <- rho_60 %>%
fa.parallel(.) #arbitrarily set
Warning in fa.parallel(.) :
It seems as if you are using a correlation matrix, but have not specified the number of cases. The number of subjects is arbitrarily set to be 100
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 = 3 and the number of components = 2 
On the other hand, the following PA will use the full random dataset
parallel_full <- rho_60 %>%
fa.parallel(.,n.obs = 500)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 = 8 and the number of components = 4 
Parallel Analysis using polychoric correlation as input
PCA: 10.72 4.46 1.91 1.48 1.33 1.26 1.13 1.02 0.92 EFA: 10.13 3.70 1.22 0.73
Page 4. Polychoric correlations of the PCA results were 10.72, 4.46, and 1.91, respectively. T
EFA outcomes were 10.13, 3.70, and 1.22 for polychoric correlations and 6.12, 2.26, and 0.83 for Pearson correlations.
parallel_fullCall: fa.parallel(x = ., n.obs = 500)
Parallel analysis suggests that the number of factors = 8 and the number of components = 4
Eigen Values of
eigen values of factors
[1] 10.13 3.70 1.22 0.73 0.69 0.49 0.44 0.30 0.18 0.15 0.05 0.04 -0.03 -0.06 -0.09 -0.15 -0.17 -0.21 -0.22 -0.27 -0.37 -0.40 -0.43 -0.49
[25] -0.51 -0.52 -0.57 -0.62 -0.68 -0.71 -0.73 -0.75
eigen values of simulated factors
[1] 0.57 0.45 0.41 0.36 0.33 0.29 0.27 0.23 0.19 0.17 0.14 0.11 0.08 0.06 0.04 0.01 -0.02 -0.04 -0.06 -0.09 -0.11 -0.13 -0.16 -0.18
[25] -0.20 -0.23 -0.25 -0.28 -0.30 -0.33 -0.36 -0.40
eigen values of components
[1] 10.72 4.46 1.91 1.48 1.33 1.26 1.13 1.02 0.92 0.84 0.82 0.72 0.68 0.62 0.57 0.51 0.49 0.43 0.36 0.32 0.28 0.27 0.21 0.20
[25] 0.18 0.11 0.09 0.06 0.00 0.00 0.00 0.00
eigen values of simulated components
[1] 1.52 1.44 1.39 1.34 1.31 1.28 1.25 1.21 1.18 1.15 1.13 1.09 1.07 1.04 1.02 0.99 0.97 0.94 0.92 0.90 0.87 0.85 0.82 0.80 0.78 0.76 0.73 0.71 0.68
[30] 0.66 0.62 0.596.7 Build dataset for parallel analysis results (Polychoric)
#build the table
obs <- data.frame(parallel$fa.values, parallel$pc.values)
obs$type <- c('Observed Data')
obs$num <- c(row.names(obs))
obs$num <- as.numeric(obs$num)
colnames(obs) <- c('eigenvalue_fa', 'eigenvalue_pca','type', 'num')
obs <- obs %>%
pivot_longer(-c(num, type)) %>%
mutate(name = str_remove(name,"eigenvalue_")) %>%
mutate(name = str_remove(name,"eigenvalue_")) %>%
mutate(name = toupper(name))6.8 Parallel Analysis (Pearson correlation)
If I want to use the raw data (instead of a polychoric matrix as input), the results become fuzzy. 7 factors and 3 were recommended. However, due to the ordinal nature of the responses, the use of a polychoric matrix is recommended.
parallel_raw <- ds_60_random %>% select(starts_with("q")) %>% Warning messages:
1: In grepl("\n", x, fixed = TRUE) : input string 1 is invalid UTF-8
2: In grepl("\n", x, fixed = TRUE) : input string 1 is invalid UTF-8 mutate_all(., ~case_when(. == "0" ~ 1,
. == "5" ~ 2,
. == "10" ~ 3)) %>%
fa.parallel(., cor = "cor")Parallel analysis suggests that the number of factors = 7 and the number of components = 3 
Page 4. Pearson eigenvalues PCA: 6.83, 3.12, 1.60 1.38 1.37 1.21 1.15 1.074 0.987 EFA: 6.12, 2.26, 0.83
parallel_rawCall: fa.parallel(x = ., cor = "cor")
Parallel analysis suggests that the number of factors = 7 and the number of components = 3
Eigen Values of 6.9 Build dataset for parallel analysis results (Pearson)
A better plot using the raw data as input
#build the table
obs_raw <- data.frame(parallel_raw$fa.values, parallel_raw$pc.values)
obs_raw$type <- c('Observed Data')
obs_raw$num <- c(row.names(obs_raw))
obs_raw$num <- as.numeric(obs_raw$num)
colnames(obs_raw) <- c('eigenvalue_fa', 'eigenvalue_pca','type', 'num')
obs_raw <- obs_raw %>%
pivot_longer(-c(num, type)) %>%
mutate(name = str_remove(name,"eigenvalue_")) %>%
mutate(name = str_remove(name,"eigenvalue_")) %>%
mutate(name = toupper(name))Plotting via ggplot2
plot_scree_pearson <- ggplot(obs_raw, aes(x = num, y = value, color = name)) +
geom_point(size=2) +
geom_line() +
scale_y_continuous(name='Eigenvalue')+
scale_x_continuous(name='Factor Number', breaks=min(obs$num):max(obs$num))+
geom_hline(yintercept = 1, linetype = 'dashed') +
labs(color = "Method") +
ggtitle("Pearson correlation") +
theme_classic()6.10 Plot the scree plot via Parallel Analsysis
data_plot_scree <- bind_rows(
obs_raw %>%
mutate(correlation = "Pearson")
,
obs %>%
mutate(correlation = "Polychoric")
) %>%
arrange(num)
6.11 Nest (Raw Data)
source("C:/Users/luisf/Dropbox/Puc-Rio/Artigo - Theory and models/NEST.R")Warning messages:
1: In grepl("\n", x, fixed = TRUE) : input string 1 is invalid UTF-8
2: In grepl("\n", x, fixed = TRUE) : input string 1 is invalid UTF-8
3: In grepl("\n", x, fixed = TRUE) : input string 1 is invalid UTF-8
4: In grepl("\n", x, fixed = TRUE) : input string 1 is invalid UTF-8ds_60_random %>% select(starts_with("q")) %>%
mutate_all(., ~case_when(. == "0" ~ 1,
. == "5" ~ 2,
. == "10" ~ 3)) %>%
NEST(.)7 Solutions
j <- unclass(...$loadings) %>% #get vector
as.data.frame() %>% #transform into dataframe
rownames_to_column("item") %>% #assign a consistent name
mutate(lambda = pmap_chr(select(., -c(item)), ~ if_else(abs(c(...)) %>%
max >= 0.3,"in","out"))) %>%
filter(lambda == "in") %>% #exclusion criteria (factor loadings)
mutate(main_factor = pmap_chr(select(., -c(item, lambda)), ~ abs(c(...)) %>%
which.max %>%
names )) %>% #return the items
#return the items
group_by(main_factor) %>%
mutate(itens_factor = paste0(item, collapse = ",")) %>% #insert y
select(main_factor, itens_factor) %>% #select final results
distinct(main_factor, .keep_all = TRUE) %>% #remove duplicates
arrange(main_factor) %>% #to become easy to understand
mutate(itens_factor = str_remove_all(string = itens_factor, pattern = "q_")) %>% #compile a better report
mutate(numero = str_count(itens_factor, "\\d+")) %>% #count how many non-exclusive items
janitor::adorn_totals()
Error in as.data.frame(.) : '...' used in an incorrect context7.1 Solution: Elbow (Polychoric)
sol_elbow <- fa(rho_60,
fm = "wls",
nfactors = 2, rotate = "Promax")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.sol_elbowFactor Analysis using method = wls
Call: fa(r = rho_60, nfactors = 2, rotate = "Promax", fm = "wls")
Standardized loadings (pattern matrix) based upon correlation matrix
WLS1 WLS2
SS loadings 7.89 6.14
Proportion Var 0.25 0.19
Cumulative Var 0.25 0.44
Proportion Explained 0.56 0.44
Cumulative Proportion 0.56 1.00
With factor correlations of
WLS1 WLS2
WLS1 1.00 0.38
WLS2 0.38 1.00
Mean item complexity = 1.3
Test of the hypothesis that 2 factors are sufficient.
The degrees of freedom for the null model are 496 and the objective function was 108.04
The degrees of freedom for the model are 433 and the objective function was 93.46
The root mean square of the residuals (RMSR) is 0.08
The df corrected root mean square of the residuals is 0.09
Fit based upon off diagonal values = 0.94fatores_itens(sol_elbow)
main_factor itens_factor numero
WLS1 2,5,6,7,9,12,13,15,16,20,22,23,24,25,26,30,31,32 18
WLS2 1,3,4,8,10,14,18,19,21,27,28,29 12
Total - 307.2 Solution: Elbow (Pearson)
```r
sol_elbow_raw <- ds_60_random %>% select(starts_with(\q\)) %>%
mutate_all(., ~case_when(. == \0\ ~ 1,
. == \5\ ~ 2,
. == \10\ ~ 3)) %>%
fa(.,
fm = \wls\,
nfactors = 2,
rotate = \Promax\)
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```r
sol_elbow_raw
Factor Analysis using method = wls
Call: fa(r = ., nfactors = 2, rotate = "Promax", fm = "wls")
Standardized loadings (pattern matrix) based upon correlation matrix
WLS1 WLS2
SS loadings 5.05 3.53
Proportion Var 0.16 0.11
Cumulative Var 0.16 0.27
Proportion Explained 0.59 0.41
Cumulative Proportion 0.59 1.00
With factor correlations of
WLS1 WLS2
WLS1 1.00 0.31
WLS2 0.31 1.00
Mean item complexity = 1.3
Test of the hypothesis that 2 factors are sufficient.
The degrees of freedom for the null model are 496 and the objective function was 9.5 with Chi Square of 4629.52
The degrees of freedom for the model are 433 and the objective function was 2.85
The root mean square of the residuals (RMSR) is 0.06
The df corrected root mean square of the residuals is 0.06
The harmonic number of observations is 500 with the empirical chi square 1574.23 with prob < 3.6e-129
The total number of observations was 500 with Likelihood Chi Square = 1387.46 with prob < 2.1e-100
Tucker Lewis Index of factoring reliability = 0.735
RMSEA index = 0.066 and the 90 % confidence intervals are 0.063 0.07
BIC = -1303.47
Fit based upon off diagonal values = 0.93
Measures of factor score adequacy
WLS1 WLS2
Correlation of (regression) scores with factors 0.94 0.91
Multiple R square of scores with factors 0.89 0.83
Minimum correlation of possible factor scores 0.77 0.67```r
fatores_itens(sol_elbow_raw)
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main_factor itens_factor numero WLS2 1,3,4,8,10,14,18,19,21,27,28,29 12 WLS1 2,5,6,7,9,12,13,15,16,20,22,23,24,25,30,31,32 17 Total - 29
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```r
```r
qgraph::qgraph.loadings(sol_elbow$loadings,
model = \reflective\,
posCol=\blue\,negCol=\purple\,
layout=\circle\,
width=20, minimum = 0.3,
title = \Exploratory Factor Analysis (Elbow method)\)
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Registered S3 method overwritten by ‘htmlwidgets’: method from
print.htmlwidget tools:rstudio Registered S3 method overwritten by ‘data.table’: method from print.data.table
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<img 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" />
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## Solution: Parallel (Polychoric)
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<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuc29sX3BhcmFsbGVsIDwtIGZhKHJob182MCxcbiAgICAgICAgICAgICAgICAgICBmbSA9IFwid2xzXCIsXG4gICAgICAgICAgICAgICAgICAgIG5mYWN0b3JzID0gMywgI3VzaW5nIHRoZSBzcGVjaWZpYyBzZXQgb2Ygc3ViamVjdHNcbiAgICAgICAgICAgICAgICAgICByb3RhdGUgPSBcIlByb21heFwiKVxuXG5gYGAifQ== -->
```r
sol_parallel <- fa(rho_60,
fm = "wls",
nfactors = 3, #using the specific set of subjects
rotate = "Promax")
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.```r
sol_parallel
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Factor Analysis using method = wls Call: fa(r = rho_60, nfactors = 3, rotate = , fm = ) Standardized loadings (pattern matrix) based upon correlation matrix
WLS1 WLS2 WLS3SS loadings 6.85 5.62 2.92 Proportion Var 0.21 0.18 0.09 Cumulative Var 0.21 0.39 0.48 Proportion Explained 0.45 0.37 0.19 Cumulative Proportion 0.45 0.81 1.00
With factor correlations of WLS1 WLS2 WLS3 WLS1 1.00 0.38 0.51 WLS2 0.38 1.00 0.06 WLS3 0.51 0.06 1.00
Mean item complexity = 1.5 Test of the hypothesis that 3 factors are sufficient.
The degrees of freedom for the null model are 496 and the objective function was 108.04 The degrees of freedom for the model are 403 and the objective function was 92.16
The root mean square of the residuals (RMSR) is 0.07 The df corrected root mean square of the residuals is 0.08
Fit based upon off diagonal values = 0.96
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<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuZmF0b3Jlc19pdGVucyhzb2xfcGFyYWxsZWwpXG5gYGBcbmBgYCJ9 -->
```r
```r
fatores_itens(sol_parallel)
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main_factor itens_factor numero WLS2 1,3,4,8,10,14,18,19,21,29 10 WLS3 2,5,6,9,11,12,22 7 WLS1 7,13,15,16,20,23,24,25,26,27,28,30,31,32 14 Total - 31
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## Solution: Parallel (Pearson)
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```r
```r
sol_parallel_raw <- ds_60_random %>% select(starts_with(\q\)) %>%
mutate_all(., ~case_when(. == \0\ ~ 1,
. == \5\ ~ 2,
. == \10\ ~ 3)) %>%
fa(.,
fm = \wls\,
nfactors = 3,
rotate = \Promax\)
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```r
```r
sol_parallel_raw
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Factor Analysis using method = wls Call: fa(r = ., nfactors = 3, rotate = , fm = ) Standardized loadings (pattern matrix) based upon correlation matrix
WLS1 WLS2 WLS3SS loadings 3.79 3.19 2.64 Proportion Var 0.12 0.10 0.08 Cumulative Var 0.12 0.22 0.30 Proportion Explained 0.39 0.33 0.27 Cumulative Proportion 0.39 0.73 1.00
With factor correlations of WLS1 WLS2 WLS3 WLS1 1.00 0.40 0.63 WLS2 0.40 1.00 0.11 WLS3 0.63 0.11 1.00
Mean item complexity = 1.4 Test of the hypothesis that 3 factors are sufficient.
The degrees of freedom for the null model are 496 and the objective function was 9.5 with Chi Square of 4629.52 The degrees of freedom for the model are 403 and the objective function was 2.28
The root mean square of the residuals (RMSR) is 0.05 The df corrected root mean square of the residuals is 0.05
The harmonic number of observations is 500 with the empirical chi square 1149.58 with prob < 6.2e-73 The total number of observations was 500 with Likelihood Chi Square = 1106.45 with prob < 6.8e-67
Tucker Lewis Index of factoring reliability = 0.79 RMSEA index = 0.059 and the 90 % confidence intervals are 0.055 0.063 BIC = -1398.03 Fit based upon off diagonal values = 0.95 Measures of factor score adequacy
WLS1 WLS2 WLS3 Correlation of (regression) scores with factors 0.94 0.91 0.91 Multiple R square of scores with factors 0.89 0.83 0.82 Minimum correlation of possible factor scores 0.79 0.65 0.64
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```r
```r
fatores_itens(sol_parallel_raw)
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main_factor itens_factor numero WLS2 1,3,4,8,10,14,18,19,21,28,29 11 WLS3 2,5,6,9,11,12,22,23,25 9 WLS1 7,13,15,16,20,24,27,30,31 9 Total - 29
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```r
```r
#library(semPlot)
#semPaths(semPlotModel(sol_parallel$loadings),
# layout=\circle\,
# nCharNodes = 6)
qgraph::qgraph.loadings(sol_parallel$loadings,
model = \reflective\,
posCol=\blue\,negCol=\purple\,
layout=\circle\,
width=20,minimum = 0.3,
title = \Exploratory Factor Analysis (Parallel Analysis)\)
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<img 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o3wrvRiXXryPONFUSK/Tnq1uJxWxIDDCV6ToPia6NX6DXng5QoBOAlfpUz54A06mOA1Czjwa6FX+jyOlHWTMSgXEMEBTgm/AfTGw+t9WKYigtcqEL4Ges3wTvTiw8sEBjieX7lUDnij2Q0/kOB1CIKvTq/abxDhzcMuFxTgWH7t9KLAG3MYwesUAF8jveLH+QJb12eFlwkIcBy+UrGQ4Y0jnuD1yI+vRq8F3oHezOxygQCOCr82eo92kqEJhx/DRPB65cPXBK/QGuvMhjLwMkEAjuBXLBcevPEneAQvQB583aFXmJZTil0uAMDB/JrpTYI3ZWCN4AXJja9KrxXeLiUPEfIDHIivUDIzvIEspl3QIHiBcg78KvRK/YYV3qP9ofAZ5QM4LPya6I2FN3RYV9Nu4T0fpBukMZw68NXpXd6L8G5Cb+8FOITftWjG0AvnEWHumbCgw7QC3+HBYMVVgWRffvpgsP72W5oHO74yvUZ4+aYuLQMJcgMM59cZesFEokz5XRp8WoHvrsRSOgWSff7hrbae3m+/pcLrwFeiV+w31AIvkxNgKL566A2GF+lWC3kxGRZ09wHv9dVHdVWnAd1ffvnlt0nRXmz4qvTOb2d4pw1dtGMkOQCGhV+94xAILwK6Yx6kBmeh6iwuhtQuvEzKenq/cM0ff1MU4MeCr0jv2sAKuxXQ27sAhvCr0XvUKXYd7d8HkgX5nvjz9DN7Wdu8XXgZuErk/eUXGV9ZQTCb8RXoXfsNVcLLZAXYz+9SuHB4k9E9rhJP2PgKfKedwMvOPNX19CZyXQivUmFWaDbiK9M7vpngFdqs87kuJxvAPnwVesHwJk71lSU0+LICn3ie0zC8JqvILAxhQSrMJnxXeh3w1kRvbwPYE37n4snwethMmCwpMbuktdtxXqNVozUY4VUM3+/U0LzQu1TzCK/UbF2Uv5wyAuzk10ivi87IKxI6tv3q97bgtSgeYTH8coLfzCgPpxPCbYJyw3UxrnLLBLCD36OwrsIsO58R5NqwFUTwLopDWO09TLFXvLV1aFWl09yFeikkA8BWfGd6pYKaKzl4woOf29GfM5mbgndUOMEKvpxepRUP4+W9RV3aUHNWaQDbwu94zmQoqLYf2DcY28lbgjVaNcPLFRiEZXzfmJpQ2dSxl4Sh5sxSATbzezz6Cwq/5haE7eQrwRqt6uEdFYCwhO8bkytlW2fYpS6YFYBN/BpXzpW2AUCMwtbgKtAarUbgHQVEeMXX0vGTN3cAz56h5gKSAVbx9RbUP+wbi+3kKcEarabgHQVAeMbX5sjQcQjUJjCLAMvh11NQz8BZErbuDECsmZxmShbDqQdhPmHd7iedXkXFQrMA8Mqvs6BWKBN6CSY/0dZMTuOTLbRooAvh774rCK+mnDCvAE/8OgpqxBIT28lPoQaXnSIls0nmZ1kIdnnNT68ibJgXgAd84QXNgK3ZaxEeyiSTGV4uPQgHtGmHnx+PMPoZE8D/BBW0ELaK1ygzkhekZErAO0pAOKQb1uXKD1yRMA/8egtaEtvFaYIZyQtSMuXgHcUJDjqH6PJlJlLw0OwpaFlsJ6dJZiQvSMmUhld3Kt/Nqlr7GulVZYVZLop47xi3FuZ2dJpkRvKClMzm8Cp3s/YtwqtqoVgqyvXwSoW3aK4mp0lmJC9IyWwOb69FJC1LXdbM5JRYlJe/vvxZj7xFT9bULIWbkbwgJVMU3rmRZKdn7VYkVV3OTOWUXBQvvCVgJniBsjWG6vQi38GspdNlyV0BJcKbA2aC1yJoZUt93pMf3mbpRYYXA2aCd1ZkZaqjDXdW46wuKnvbSyqMCV7xcxGWdwdvwLpv6V99X6b2C69q89UiMsxHwP2YzcEbUH04WYqAt1V6fQUNqtlUmAF3wlcM77TIpWwWqy4XrK5MAU1djnzkF6Ck0ZUdhe+aoYWGC/7aZRmSGRe5lM1FYHXmSjbsDV57Sfu//W35gNEAMHrX/Mw0XDMsvJcpmYt6LbYotILfsO3t0uvaLuAb1oOAyBh4lfwMNDx9+49W4L3e6eYt4LUUz1XoLks+sstS0G++4X9FfHECsFWGE7bx2vy1EXjPd05zQRl/T51zobtMOcksa0FHehV8MwMsNzij4cJmoKOvGpnlhO3BZS4szbVvGn+XKSO5pZfr8Jq9TvRq+OL3IETXy7uFhjYi71n+liF6iRJgIRlZXa6cZJZeUA7vQq+Ob74AvGZloaENePN5idR6zxR79+jbvcubm4ySCsqInOh14ZsH4GbHefN5iZdw358X3obpXQs64TjSuwZfM774PQiCN5P2TS8DcPzPUdToteCLHIAJ3lzaccdhGqoaXo4KvQB8EQEmeHNp16F3hlcJvVLwdeCL1IMgeLNpz/RK8FrpdeGLEYAJ3my6CXiXK/Jmet34pgJM8ObTjunV4RXoDcI3pQdB8OaTH95m6Z0eTyH0GwR6leDrxTc6ABO8GbXf0LvCawi9Gr0AfKMAbgveTVeJDNd+Q68Cr5deEL7BPYimVolsTrulV4BXmEQt0huHb/aJaBFKh7exmDtrr/Sq8Or06sEXim8owLnRyJ0CwVtYIrzi/StueuH4hvQgcqNxs/DulV7p2cOW0GuiNwBfcAAmeHMJAG+D9CpPfbeEXkPHtw/DFwQwwZtNuwy9BniN9BqDbyC+3h4EwZtNuwy9CrzSXdsAekPxdQdggjef9kivCd4gesPxtQNM8GbUDjsOC0H+0Gvu+PZR+Go9CMCKZQRvknYYep3wqvTagm8UvnIABqxYRvCmaX/0GuENpzcSX2kBHYI3r24AXmWhLTC90fgKPQiCN6t2R68ZXhe9GfCdASZ4swoCb1P06vB6Qq8r+CZF376pbsO4Eit7xV8bJZv2FnpFZpc38fSmRF8NDbZ6zlcfdGt6+ukpjCuxXuTVefcAb0v0GuBVl5cNozcFXwWNl58+GK3p6eOkcHlgC2Cf0dcDzKed0WuD10NvHnwVNJ5/eCs+1aY2eIdvGPuF+LEheHfWcTDBq63srdPrDr6x+CpoXF99FFcdrwzeeV3ey97gbYdeK7zu0OujNw5fAxpXTDRQT9jYt4otg/0Os1eeXXuiV2Q0LPT66I3BV0Xj1FcbeaeVWIc/DwZrvboReP30ouNrQAN1ICr7OG/IPU8baUf0WuDVn2djotcbfEPxbWic12zdC7xt0OuCF4PeMHybh7fCO6Y17Sf02uAFhl5/1yEI3/bhFSYaJfvKpd3QC4fXQi8g+MLx3QG8wvIttQK8m46DAqz4HpFeKL57gHdWxfzuJfRa4TWE3hR6YfjuCV6mSvndS+h1wwulFwvfvcHbV8rvTui1wxsQeoHB14/vDuHta+xA3Aa8yPT68N0nvH19/O6DXpVX+ZNe26n0uvHdLbxMNfELg7d2en3wBtCLgG8D8CatY1kPv7sIvS54w0IvPPja8a1/idNk1cLvDujVaFU+ZqI37WaheCHB6/mOAePvtgDvoOPghtcYenHoVfFN5AGoMskAvFTAb/uhV6dV+RhKbyy+6TxAVA28TBvz237o9cBrDr0uekOC74wve71BePuN+W2eXnx4g+gd8WUvtwlvv2UH4ibgzUrvQO7fbhrefjt+W6fXB68l9HroDcf3puFl2oJfILzV0guCN5jewI4v063D22/Bb+Oh1wCrtsFcn2j0EryrSvPbNr0weMNDb2DH97b7vJKKdoDb7jj44Y0MvaEdX4J3VUF+mw69QHhj6A0LvgSvrEL8Nh16AfBaQy8qvQSvpiL8tkyvKdDqWwrQ2ya80zLC/fMfP+J76Ut0IPYOb3zoDej4rg0+AXE54K5umiWZcRnh/np4lQfePj+/7dJrJNWwKZpecPBdG3wE4pplyfEcyVweXv768uds8DJl5bdZemHw2kMvHr1yg18eLj+2EHn78bvW6/Bio5aP31uAN55eEL4SVgMQbHle1NVNMyUzLiOswpuFs1z8tkovEF5XY/jpBQVfEasZXNR1pbMkMy4jrMGb7Uc+SwcYCm9t9JrDrGlbCrwQesUTtmnJ8QYi77SMsBHedvhtNPSGwJuX3hWrCYhLjgeclRrnnaorF8HI/DYaeqHwOjtxIHp9+LY5zms1C9WVh2BUftukNwjeJHp9wXdn8BpvBswzAIGQ6s7hdZ8/I9C7N3iNQicYi98m6bVEWePG1NDrpvcm4OXCJhiF3xbphcOLEHqdHd/bgZcLl+B0fm8A3lR6HcH3xuDlwiQ4ld8G6Q2A13PVKJXeW4SXC4/gpA4wGN566A2FNx+9NwsvFxbBCfw2F3ptHQTb3gjwjh1fHeHbhpcLaeArkt/mQq81xlo2o9A7kGs4c2sL3oyrAmIQHMVva/SGweubKwWn9xud3qZWidSSxc57OsER/DbWccCFN6DnMMBbBFZVmyQb6zSV4NAOcGOhNwJeBHq/4crT4B41BS9XGsFh/LZFbyC8OKH3G4I3VEkEw/mFw1sDvfYQa9uO1HHo8zd4Pcli3gmfcCjg4KZCbyi8/ttb4PQSvDGKHk4DdSCaCr1R8CLRS/DGK45gAL8t0RsML+DOQii9BG+iogj28Lt/eHFCL8GLoQiCnfw2RG84vHihl+BFUzDBDn7bodfRt7UfgkQvwYurQIJtHeBdwwtZTwNEL8GbQUEEm/ltht5YeDHoJXhzKWQ4Tec3AN5N6XV1DlxHEbz2ZNlip2ydS/w1JwIFJljlt5HQmw1eCL3CkklsSdPLtPaMasVV9mT5YqcXfYXLLGuP+AUkWOpANBJ6nZ0DhymR3s+f2evS4Mtipi9/+bTs0yi842Knl+FLeBa/iPEXdjEEajCB3zbojYMX1hQOej9/ZvhKHPFVyX7+sG5oFN5x1TL2W/KjAO9RUJ4M+AVxPmexiY5DArwp9H7mEjnia9xeheV424aX6aJGXpPy5MYuv9PgjHVpOYpXJLzxoffzKrHBxzVuxcDbNrzD1/D53QfRaqN3C5J93gKz0yFkKUYp8ELp/Syqnzf10gkbP7d5/tMn4eCm4WULXT4o1qm+IBQXAdnpJiQb3fq26LCK+/vnPNBpnlB9vfKqmNnrUtJpSdOnP4j7NAtviHVzkq3JPwbw2/HX3DdwaUqCV7YbAqxnwGyn47zRTjcD2ZTuo5glXwJdLyFbiN9oeHmxjLzKctFL8NpVPiSr6T2K2z2eOq2AJegNh3dmFVh3BC+C03IkC+k8KltdDgzlK0AvCF5zgAVW10DvawvBBG+ECoA8JfCobbOka+4k5O862Eo5xlZnhwBaR69fE7y52jEjyYYjbalZSlcUXi2+AkazAS4I3kIjSOggP+oRypSItXCZSy2dcxmsnoMBdfH6NcG7wawynJD8KCSmJr18tncP8DsOUgfWN6DgTgr2RSZ4t5oSOSua5Ec1ESVB/sFRNpRiW0e0SsBLJ2y9Y1W2PLmxKwxkdX7Oalt2dJYgsniAIdgeA14AvZHr6TUGb1WFBCouJC/b+BskeGG8KvlIMQNDb11BqTQuNfcnJIWBPH1IgjecVyXDKWZg6K2r+eryVxG8ooAhOTzyRgRYRyZTzMDQW1fz1eWvUnhXPXpIFgsw3s0lHX7A5VUSBrxeeutqvrr8VQ+vcs7mhPcq37jHdMDlVclLirmHhd66mq8uf63BO8nea7go8ObKVo8Er2+nupqvLn9VwxvR5ZVu5Bp0+E+jkLKXZgeF3rqary5/NcALYVTVerRUgrPKrsWlGelAqnHg9exUV/PV5a9gbqIRtd5JrIbe6W4uQcHFC6E6HV5A6K2m+Sr0h5+bpDBqlAHe5TgJ3rO8akyPWTwDz8ejO1gD4XXvRfB6rBFTFiMQjZ/iq0/sFd66Liblvfo9ZcMarCEldtTL+LUgeJ1WF1ZFGbVLvJ9Ny1ruiTk2eUs6h2ZXF8QJL9uR4J3EVuAbflu/kpYFiuEzD6J2aS7FnFQLr3UPKTofRcS1vdYiTFdg1OYrq+388RX4rl9/ugpXoQ4alRsyatKYC/uVCtfshrxVHQ+vvI+4lx6llzKMV2DU5gvMc6o28zeuwPf07SdxLHTrFfgcEr89hpsxJ+PR3us9HH7Nm7/0PVynbErkZbo8aM1XVhv640vpXKXL/54+7zYyBH3xngrhR2F6Z6xTtjEnvTjw2oOH3udl2GrNV1Qbw3u5659+/1G2VgSvLRA9LkaR7PmtKfaO237Nhy8ivMb9tNEGdgXG1HwFtTW8p/G8baPc2OXpYz/qPXHxvVaOZUM2ekHDuKB0XLsJJ2zsCszGzbcxvOykVV2Bb2MBTg1N55Dih6MSfA+HNb1cwRcTXvuOS+tZSbwAAAf3SURBVLHGKzAbN19d/jaGFzSiYRz9UEDux1ti+uWvmGoeerHgdVdCXc1Xl7/N4AWEW3FHdXeF5PmNcPdWdnqR4NWKJquu5qvL3xbwQrHtZXK14bL1Y+95m6XrQJF3a39lcwMOt8Le6zGPkkHc0fhWHkTBpxcWVmEpEbwx/krlJgzb9QjxMGmsV9wT8D5D8MWD17VfHc1Xp79DH7viA1jB2PZ60B21DvZK+8I+oAdfFHi9lU/wOq35qic83AqHGQ5+7E1fBQevKr2Y+ALPNj07bNg6MarLX6bqicS2d5DL9GjY7MJVSwGRXoJ3c3/41RON7XKwffDIy67nI2bwJXg394dZPfHhVjzenorR4qFVTwiLXuhAgttO8Lr9FTglSMW295M77aEtGxn4uUcLvqXgzXw6HaYaZhNISoM3HdseQu78/VDg1fb2b+iRgm8heOtSYxmyWxHCrZiQO7nFqNxToe2nH2lIDSP4Erw1KKL+sLDtYeSK3xP5TmJ9T8AWpnR6Cd4aBKg/9Z5dLNcgcpXvijjFwbAraFOPEHyBteDZjeBNk7f+RnRwsWWCkas6DobXdqNIIr0Ebw3y1R+ArwgBg66hi7LOzzHtDdzGlBZ8Cd4a5Km/HOiCyTXG++WhxKb9jYnYUk+hl+CtQUKGptujLifJigwvnFzLmeE8u8x4gDkZW/oJwRcb3jO/v2fbNUW8qjhDfFUS9uekWBHhDUbXsNc4u8x8SMBWrmh6keG93rHQsfGaIl7Vm6FxVZL+6dt/qPBiKYRcx4BcMLxOeiPxDbmHyb6DWL0DvNXe2z2p5gwxeNn3Pwu8YeQ6B5Mfgyl1eYyiFxx4wfCehx+8y8O4MoxurUM1Z4gv7CAvcouV3UBy3ddBHoMhdTqNCb4hd+E5zFL1Xk4UeQOlwDsIPfKGBl3vNbzHYEjdfsPpxYaX1fnlRH3eQOWGN5xc/wURbXbZYrAf4vQYHHwDyuKySqMNdzTaEKqsQ40R5AKmTmizywSL/Ri3AukNuAnaZaRx3jSB6y98amk8up6rbtanrDiO89IbhK8noEKriuBNExzesGSiyAXNWGPmcHj9i2GG0AvtDXisBG+aslR0JLmg6T+GuZGKzXWcSwH0ErxVCL+iY8kFThSOhRdCLxhfgrcKYVd0IrpAdm0PJQYd6hCUXoK3CiFW9PEYTy70/gzTrHSD1XOwXcDgS/BWIbyKTiEXPNndOC3dYPUc7BCIXoK3CqFVdAK50LAr42d6rmvA4VZBgi/BW4WwKjoF3Sh2Y+AFPjzGTy/BW4WwBtTjyQ24G1neS6cXCV5P8PV+SzNe+NlU1WUIrGxRIpbdGHjBz+0C0Gu3NxZQwdprzqPLFRCxbXcEOfYAJGKRK/j6skzw1qY8LRLS2SgKrzP4evJM8NYmIefG58fHKKijbLudzb0LJBmL7MEXDO94X6U0xXwfCDSmNefG58cHp3cMC7tm6Hwr74ETMuvX5SUojXWOOb+vcr61VbU2px3kfLxT03PLiuc8+gA4Z1e0Bbws+LL46y+NJPHzUEnTra0ma1vaRc45vO6bBT3lPIT1GHorcp5lI0OSMuvXQf7SWD+f+Q2BBO/GUuH1RF5fYjjsRsEbGHuT4B3XcCF4N5YCr6fP62vukMDLF/qzGT2LnpoTDBkxY4qFd7yvkuDdXAq8ntEGXHgde8bA6xstWPVrGrzTfZUE79YKG7wMbG6n3JyL9OLckK4rpdsQmljF2mvOs8Pr6jc8CrsBrhCHz8IgeLn2mvPc8DrMj4+2xxJHJqiL4OXaa87zwuuyPsrwYiSpieDl2mvOEeCNmh/4+LjCC42o4Y4IXq695hwD3jj3Mrxut7GOCF6uveZ8O3jXPi+0N0DwRmqvOd8QXs9DVjAcEbxce825s/3k6xm2xGKaPHDGTKwjabLC4aF/eX84RF9e3CsCNSseXuVKsi2xKHidx0Qd5M7a9PAIthzpg/UQgrc2xc8KfPr2E2ttm9m1zWctDm+/PjTJAW/MuEkDajfnYZLKeT0ogbdleMdJjr34dbzJRt2xxHJe7vqn33+0ml3bfNYtIi+fJ3a+s5r3q1sspzL1VzW7tvms5fu8fJLjy/sHs3nfusVysnPzB7vZtc1nLR95+STHM+u64j8zqXZROa3mNuCNyMVuROW0mgne2kXltJqVbeLzu60JIsCb3h2nRt2ZkuGVnt9tTTAdXnlNBVDWQs27EZXTapa2yc/vtiaYDK+ypgIka8Hm3YjKaTWL25Tnd1sTROg2ELxgUTmtZmloWB6LsiYobT2DRuQI3mhROa1mZVtw5J0WBgs7iOANEJXTak6Ft4eNHBC80aJyWs3p47xnZYSCxnlxdTPlxL7LEcYhwuCwMWt7neQYplspZ4RS4Z0XBgs6KNR606KqsSo58k4Lg4UdFGi9aVHVWFXx3AYSF1WNVQRv7aKqsYrgrV1UNVYRvLWLqsYqgrd2UdVYRfDWLqoaqwje2kVVY1XMVaw4eOlyWZyoalBFkw5KiqoTVQRvSVF1oopmzJQUVSepWRG8pGZF8JKaFcFLalYEL6lZEbykZkXwkpoVwUtqVgQvqVkRvKRmRfCSmhXBS2pWBC+pWRG8pGZF8JKaFcFLalYEL6lZEbykZkXwkpoVwUtqVgQvqVkRvKRmRfCSmhXBS2pWBC+pWRG8pGZF8JKaFcFLalYEL6lZEbykZkXwkpoVwUtqVgQvqVkRvKRm9f8COmkcDvjnnAAAAABJRU5ErkJggg==" />
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## SOL PCA (Polychoric and Varimax)
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```r
sol_pca <- principal(rho_60,
nfactors = 2, rotate = "varimax")
sol_pcaPrincipal Components Analysis
Call: principal(r = rho_60, nfactors = 2, rotate = "varimax")
Standardized loadings (pattern matrix) based upon correlation matrix
RC1 RC2
SS loadings 8.21 6.98
Proportion Var 0.26 0.22
Cumulative Var 0.26 0.47
Proportion Explained 0.54 0.46
Cumulative Proportion 0.54 1.00
Mean item complexity = 1.3
Test of the hypothesis that 2 components are sufficient.
The root mean square of the residuals (RMSR) is 0.08
Fit based upon off diagonal values = 0.947.3 SOL PCA (Pearson)
sol_pca_raw <- ds_60_random %>%
select(starts_with("q")) %>%
mutate_all(., ~case_when(. == "0" ~ 1,
. == "5" ~ 2,
. == "10" ~ 3)) %>%
principal(.,
nfactors = 2, rotate = "varimax")
sol_pca_rawPrincipal Components Analysis
Call: principal(r = ., nfactors = 2, rotate = "varimax")
Standardized loadings (pattern matrix) based upon correlation matrix
RC1 RC2
SS loadings 5.40 4.56
Proportion Var 0.17 0.14
Cumulative Var 0.17 0.31
Proportion Explained 0.54 0.46
Cumulative Proportion 0.54 1.00
Mean item complexity = 1.3
Test of the hypothesis that 2 components are sufficient.
The root mean square of the residuals (RMSR) is 0.06
with the empirical chi square 2046.33 with prob < 3.6e-207
Fit based upon off diagonal values = 0.91```r
qgraph::qgraph.loadings(sol_pca$loadings,
model = \formative\,
posCol=\blue\,negCol=\purple\,
layout=\circle\,
width=20,minimum = 0.3,
title = \Principal Component Analysis (Parallel Analysis)\)
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<img 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3g31t86eMlOI3nH/7gFUXypL0FJ15uLl7ElBG9uqwmuNxlvXuHtDzPw+cJN9Nf3CN6d9NcOb9XCO+0ycPlCxZfxzVNV9SqsH86WELy5rX1Qval4swqvvbvL5hu5j0W3g/UK3k31V4wX1AvjZXTpxnurxuQbFF8u3S5dL4RXYZ2wtsRN4M2ceIE1mqzSG8ebU3jDwwxcvvaNBLodqHdDeFeZgW/p1RJPUjHWXRcvo0Mn0UNkPL5z8U2jm1x6c/DytkTLopSeVVYLtTILIaYXwFut8EKHd1P4ptLtapVehfTA2xK/Qg2Cl6mpJl66NzvYlThMvjl0u1S96XgL7QreroLeFLzJhZc4q8bh+z73Qt+43mXxwnYFrw4LVD28ZFd26DPCFF9TdRfQm4y31K7gNSnUm4A3tfCyrmbA+I47DHnFd3W8mF3B24djKhVvjcLLvRIH4mvv666kV0GrLrYreIc00Fuh8CbMARnj671Nyyq+Ub0JeBW4ZsaWwO0K3jEMVnXwEp1YSZx61+cbOcLQVm8a3nK7gncKrbccb1LhTZ961+YbPziWU3xjehfBS9kVvHMK9CbgpUYxJWva6JEvfFw3gy9Xb2W8pF3Ba6Uu3sLCmzvlueaLn5JI1ltUehWw0gp2j4rXTMX2dPrkVbQVSH7p5eMlBzGkYLp+8mxacvEtKb0KWCe1KRh2/Rdcz4T02ZtYa800X62Ziu3y2ZtL2nMh9ZbhTSi82XbN53vITwtV0FuIt4bd4AVPmUAxO61X20/F9vz1G/10UjrN1cvGyxiDTq7duegSfFOLL09vPbwsu/4LrnPePd5hTpWL/UeE1ymltwQvu/DmfjuVu79A8U1bd6i3CG8Vu+FUOl1qtcrIMnjPd93zH3+OtSKppje/8Fahq4PzTSu+uaVXxVeHbwqm3RDv0128tWYWwnvvTKHN7JTQm4+XW3jz7MbfpRF8UzrILL0qurI6dv0X/OPLR6C1ZpbBq998JsynNyZLLw8vp/ssu/ABBpRvUvHl6K2Cl23Xf8Gf9Icr2FPX5majx3mH4Hpz8TILb45d/NgYzjehm0BvNt5Kdo96nLeo0wy9LLyMrjPs0h+SwPimFF9abwW8CXYFbyyoXh7erMKbcZiB9/meOnxzSq+KrKeWXcEbTbJeDl6y11Z0dVC+3JVklF4VWQ2yKZLs3hLelKsRMb05eDmFN9lu2qcqEb7s4uvrzcJby+7Dww3hZUwwPydRLwMv1WOq3fQPBGN8maug9C6I9+GmKm/H/ay1CaKXUXrTC2+i3bzPssN8ucXX00uVXhWuoY7dBz2Q28KbwjdNL4mX6C3Nbh5dHYQvbwWE3hK8fLsP/ShuDW8CX1hvKl668CbZzaerA/LlFd9SvBXsPoxjuD28/F3fFL0UXrSjpENkZXR1YL6cR+N68/Hy7U4/HQovd9JAbvEF9abhpQrvsnR1IL6s4uvqTcRbbPfB6n7Ps0QSY8dnGWH1wNfr4k0qvAl269DVAfkyHpugV/mPhTYF0+5DfB6JPgUeErLMaqiJGjhdQHpT8BKFl22X+hKUxAAft+AUX0dQEt4yuyjdQg/sbAEvky9XL44X6YBrt67cPrl8sdKbhZdll6B7W3h579wAvXy8eOFl2m1BVwfgSz0MKb0o3iK75BK3hZdVfOP48P0GDy+4buZhhlZ0daJ8yeIL63XwKu9h8U3BsUuW3e7m8LL48vTaeLmFd326OnG+xINsS3DpVd6jopuCYZdD9wbxcviW4oXWy7Lbmq5OjC9VfEG9CN5Muzy6N4mX5ssqvQBepPBy7C5BVyfKF31ELbykXS7dG8VLvnOLCmTjBVbKsLsUXZ0IX7z4QnphvHl2qQXm3Cheqvgy9MbxwoWXtrskXZ0YX2x5i1U2Xsouv+x2t4uX4htDCOJlFF76MMPSdHVCvmjxpfUqe/F0u0l0bxkvwZfUG8ULFd5N0tVJ4zvbysOL202ke9t4cb4Rhyy8sXVRdteiqxPhCy8c1QvgTbSbTHe/eIepcc738WZ2FNLE1jvhBQovYXdNujoBX7j4EniVvWywKXC7WCMQ+wUf5rjNmXUmoZcqqzEzXOr/lOLFim9IkYE3sh7c7tp0dUK+0JIxvXG8SXYzym7nvODjlKcZ830l9FJlNcMMl89f/70YL8YX1zvhJQovancLdHV8vmDxnZTFSq+yFvQ3BWI3j679gk9Tnu4Abz9V1XWglwp4Eb6BRhJvuA7M7lbo6gR8geUiemN4+XZz6f74o/2CD7NG2n+KN4337M6zVtILxBfTG+CNFV7sENmW6Op4fKHiO1pLwgvaTaP7oxX3BZ8mm64+8V4bvNfUqbw6CrjbA0ng9R++I7o6Pt/oQmHpjeBl26UH5YK14+PVGnaL96uvClYOFF9Yr483Unhhu1ukq+PyjRffoPSSeCG7YNmFwc759tug8j6dTvVnSl/sOO9XXxUAjvP1TIZ44cIL2a38+Z66cT8tlKZXjXewCq9L90cO2KnDa/Z7nBdpLgAc5Qvp9fCGhRewu2W5fWy+0eI7qOPijdrVdFO8Tunh6hwQr0424Bhfl2VQeme87sPidrdPV4fi6+kdMKmxGbPbU314SAI7Zoarc1C8OpmAVeSuuF4Hr19444cZ9kFXx+EbtKbg/TVSYXOOjrlwdQ6MVycHcKT4OjJBvPYjdk5Xx+IbFl9Xr4fXbApklyD9yG4IV+fgeHXSAYd8o3p7vNHCG7O7L7o6Nl+/rffnll41WFVqBhvu76bSjcPVuQG8OqmAA742TgCvtXTE7v7o6sx8g+I76O25ftuj7VvsTRHYTaMLw9W5Ebw6aYCVf9vV+099ut+beIU3tLtPujoW3+m+4T2X/ufLHpg2ptSwFaxNEdrl94zD1bkhvDoJgP3ia/n85ptver1dj1cRdvdLV6fnG9mFNRC/7L780sGrELvsskvD1bkxvDpswB7fSeg3Gm/n4Z2X8+3ul24A1t116PF+OeIdNpC1MTy7TLo8uDr7wlttVkAmYJeveVm+6dNpvfrOcadhXNQ/RLYzusB5rnHnwd3zffiyT9dzG3caxo3h2mXR5cPV2dUskXXDAuzw7V+XEW834B3u7xfZI13Wea4o34eer0anbyrzj86vv3p2GXTT4C6XcryNfscYgJX981R8x0GZgw0D3Xe+3Q3TzTgxO/Gd7nl46PV2+ljZ+CqYjfHrr7+6dol1l8BtXX5br6Fo/RRgu/gOJfabb8btYv4zLPHO3WXYHN2sKwnsDHyH4vvQ57rX21kbo//2OxcvXnZLK25DGousoXj9OOCJ77R/4HQ4/Ha/c/BuhG4xWDcj3+Efg7dzq5u58aulF6NbY1fh5vHqYICttyLKf7W64Y53lt5V6VYG66bney2+ff19eIhuDIP3oV8AWlOtfVzBOwQGPBzB1P+P9Xbq7b4zaJenCxwkaJKRb683vjF03dVVGaJb882Z4LUCAY7uMkwjOJmyq9kuRXdBr16ufH8b8MbfEOk7+x3iSGofVRC8XmKAx30GZAzv3zf+kMR6YN0Yu1e9yMaI4m1xOEzwRuIBHvd4kderjd2tgLXzmwn2mzwei5jT6jiu4AViAf6K6ur0/n01vVsEa6fH+xuyMcy/k9aWJyAEL5IBcK8Y66lsFEu+56oUamP0YlufORO8RL76aiBcF+/+vDohNsZ4reSKoxC8Jr1etKO+kWK4c7B28K2xDF3By0hfe8lhxEkeCKwVYmMI3sgahplYP3lltaoF4u81fHx5On32xh3kjz/+6U8/9jeOCdaO+6ra8zOOrd9+/vmiwxgn6bVsbAtvPxPrZ28uFpxF8PoHeS931w1lzWV8bb3SveI9Mlg7zqs6zJjstH7++bJ4zRg+/vVVvLV8/cVr6GdiPd+7M7Eug1cp/4mcXbx/uqk4f4bGCXLnjfH5QvFofPjLi7oTllVdg8H72Nkbaym8/hO53Dk3T51+TX8sfrI7ibsxArym8C6722Cmivz0Z7umbBHvfYs5sJEYun5HT65d3XrF23wsWwmF1+w3LDqMcQyXmvOcVsfr7/MWr59KBO/Hl4/eQrr17Z/eNh/MRkLjVei3hdUfxjRJ76Yrr3+0oXj9ZMJ93if9uQF7fuDu9Nak/WC2EQLvsKe15DDGSXqrzu1/gOO8wz4vflLptvDiZ9im9yFrjkLwdtbLQJwRvS29xMaw3+muNIobx+u9AkhPpsnQPTzg74YQW8M7VNMogjcae7t/ob4woa4CHNkeGzCJt28ZZ9BpCljwBgm29xcE3tNPfay7jgsYOO49x21oCljwOolvZ2MX7Ov6Vi7Aq3NMwN+NeKGtEd7VDLDgnQJv394u1Nn13phdk6MB/u67UW9wvrwP9Ho0ASx4TbDteoWr8f7ud7+LlZv+LgivznEAX+l21o5DdGMgNqsDFrwoXEO303B1usikI/1/tF2Y7zEAj3T7Dda9fh1s/NN0lAxcSVXAN46X2o797kI38DUd2j3ON36a/gGzb7893Xk6yNdXvLGNwVBZDfAN46W330S36/WaB42TIsbmIcSKr85uC/BIV/X/Gruvh40xbo1umhmLscIqgHeAt8U8lqzt9oV9w+AdH2E6/iX2GEJvt0vAA91hzle9DTTeYWPMgNV0cJe32mLA25/itHqY2+sL167m6z7ql7hemu/OAE901fAf/d/erpqK8dBi7kuhWHUfuHYq4SV+x9i9sLeTS7f73fzY6b5f4np5fHcDOKSrf3jtQp3+tW+ykwG4lgeil0VWw+klZft4dI3dcR3jfb/8Aull7DsM2Tzgke44S/xot3O3p/3vsFhiRw5g+sEVPDCyDbxpv9g+3cmu86r8gull89004JmuGv/b//DavWzJqcLOgklJAHwreBP/IHnv03Rmu/bXVGB4E4qvySYBT3SnZ23ZjeG1N0+W3o4N+BbwJsONlF3A7jWgXJ2U4muyMb8WXTX90P802TV3uot0nbdwTmjAR8ebATdG17abgje1+OpspwDPdOfnbNvtpg07/Ku8hYs/xYYDPjLeLLhRuohdWm86320Atumq6Qffrrmp/MXmtRTq7TDAR8WbCbeL7Ox2rt1UvDnF12RdwBZdp+z2P792b6qx2X9AV+kTxHHAR8SbDzdednG7NN684muyFmCHrpp/Gn90C2+At77eLgb4aHhL4AJ0Xbs5eEv4rgE4Tte3OxdeHG81vZ0P+FB4i+BCdCm7LLzZ+w5DFgT8nU03vvc621XOUjZ0e5V1T/nOeg+HN3vlAF0aL1dvGd+FADtyHXW+3bDwgngr6+1GwIfCW7JuiC5tl4m3tPiaNPbr0gX2XC27yl3Ose6sqMXlNnvG6074VNgLWHY9u0V4y4uvTrsC7NNV9s/zraDw0njb6HVecDPv4vlUd3bTVqvxptor6gWmy7HLx1ul+Oq0AOzR9cvudDMsvPahtPjjG+m1XvB+ynF3uu/t4n3++s0lnGE0Jwhd324x3jrF16Qu4ICucm7Mt17P9013zj9Yj7JX0LXRO7/gw5TjP+yk8l5/17zCm9cLRpdnN01vreJrUguwTxfeY7XtqmBhl7y3yvp67Rdc49XzJVed3bTVas533fMfwxlhU4PRDexWwVux+JqUAw7pKvfWfPO1ded0r7IWtR8XrNW/pzQ+Xg236rzSrVbjzY2e1wtadtl2E/HWLb4mJYADutjeaqzwQnjb6/XxXvZSefUXST3CzZzgdEO71fDWLr4meYAjdJV7K2bXvdv6yX1suOrgrqL4ePXRhqrzSi+4mrReCLoJdtPxtuGbfhiYoovZne+3fvIeHa49uKsk+z3OW9YLRTdiF8abo7f+vkOfhAIc0sXfZL22758brEUovJX13iheim6a3Sy8jYqvDgtwjK7yb9t3uHbnFmuZYAWRLsL7snOTeMmyG7NbHW+z4mtCAI7QJd5gvXYarBZ7IbL0VtV7g3hpuql2c/E2LL4mIOAoXRXc4dwDFV4Mb2O9N4eXQTdqtwnetsXXJAI4RjdWdp27wMKbirei3hvDy6GbbrdIb3O+HuA4XRXcgdq12pzFwvVEO4vdm5HbwsuhG7fbDO8CxddkABylSx/Teu222Y3Ogiy81fTeEl5W2QXsNsS7SPE1eQvQVeE97l2+XbvVWZKHt5be28HLo5tntwzvQsXXfL4n3AWOOApsIYWXwNtU777w5s8KyKQL2W2Md4HiaxVdB7AKFyXtOs3ujWB1kfVH+8jJrmaJDFbLHTuXbq7dcr2N+Qb7CwPgGCHULl54o2U8PqIsvYtgDTpdY7VzK5cuaHcBvC33HeK7ulfAKjwM7OOM2HXavYXZpTdLL/cFr5pV8bLLbjoFl1wAAA3HSURBVIHdGnhbFV+Abg/N3wcm7Ibt3tL80puj99bw8unCdhfC26T4gnTnJ2UBjoDCC28B3gy9t4U3gW6R3Up4qxdfhK5ybo67wMpfjii8DLwV9d4U3gS6iF0O3lp6qxZfmG7sKV13gTl23UX8ByThjS6N5YbwppTdwsJbD2+94ovRVfF7lb8L/DpYwnukv6LomqO9IQMBc0N4k9ZVWHjr4a1UfBG64Dnb/n4LcMSu91h/Vcl44bZIBG80pXZr4q1QfFG6Kn6vfX8P+DW6TH8Xb+XIYOC2MII3FsQuE29VvYV80+nGEL19+/qtvwx5yWMq3jS9gjeSCnbr4i3Zd8DoJp3veu2fSaYLb2O9gjcMZnctvLnFF6eroPsjDeNOwwg4Unhr4E3RK3iDVLFbHW9W8UXppp3rcnZ4td+IXTbeSnoPjPd8j7WCQe2uiTe5+BJ0FdgQafHfrEULbx28fL3WS6qnSzrrq3GqT++EdNputZdTFt5KdpvoTSq+OF2s7MaaoniDKyFiq0vrflw31jxlfknNlKbXfPy3N5HWqllitc9f/z0HL253bbz84kvRVWAD365Z0AYceWQWXq7e6SXtpzS95m+vIq11s8Bqr39GLhl469ltg5dXfL8j6CZfXhDYdZFP7+FiK0wdAjYOL9ZL2uN1pmjeL15v/4fZKWF3C3jp4kvJRU7CJtl1F9WAIw/OxMvTG+C1C++O8XbO1KzMTmvabYaXKL4k3fTzW6FdYO9ChZNCIL8o4DCwsTjx8X745zfx1prZKF7KbhrelnpBvgy6CmmKt3EKr7lX/xNezg71Bo4DH40VH+/zPwKtNbPN47yV7TbEC/EtpRtv5Bfe8Qf3PBzUHziSuRNiiQMf503slLS7JbyxfQeaLnFaNt4K2I0sbN81FeDs/QaGXsE7hLa7Lbx+8eXQVVgb0BixC0H373vbn4gDu4RHQw1qiODtU99ua7xO8WXQzTslC9mNLR67762KfCSZMSBiWH0ErwnDbjLeBfQOfFl0FdoItMbscgvv1C80tSo2ImpgJoJXp4nd9nj74suhm3s6trTwTr80UcDooKbO4EbB2/HsbhNv9xOPrsJboeaUwovj1QkAo6OaewPbBG8zu0vgvdJlnC9WaGOG3egD4muJnIhjDmzuD2oSvDy7m8TbV13qfDFZdqH2qF34AcBqwqWtSU2QgdkdAi03hLdoQjaVM6C2eucdBowvcbQJqWuw3ehDoPVEl0Yu5QmTOZ/ezvA2fJIqZ0At8br7uqBeha8F26OsU3jh3x7gUp4wLYtSehqtNrM/zmhUVr/t8AZv0+LFlzpFlWc3/hhoTegY3irGV8Stsnewk/72hzd6hCGiVxHrSbeL7CJDqyJ2uRnfcSh4c1tNVF6/bfBCB8f84ssou/ASiF3gQdC6qJ1u8y8KWPDmtpqozI4b6MWO6zp6FbGiHLsZhZeHVwcELHhzW3VUbse18VKf75mLL3k5IX7itV7hpf8A2DeigAVvbquOyu24Ll7OybRBr6KWy7KLVWtwdUl4dQK/gje3tSuwWxUv6zxwX3zpzyDk24UeB68vWa9fgAVvbmu3DbxMujo/KXKRPLvobjK8wgy8OjNgwZvbWmK3mt4Eulcr9PnifLvQA5EV0rvfYEsPWPDmtm4Abxpd/S/KN9duZuEtwavz9q3gzW0tslsDbwrdebCwXpxuZuEtwkttYsE75el0eoRbw6iSnovxptFV889Q8W1jdxm8H1+eTp+9ub6Cn7Sf1YkezQr9Xe7MjILs0aiingvxJtH1hwpc7aBid0/BdxrgxyJrpfESG3l6gfRsTk+Pl8/eXP8Xti6UlftbEG+R3kS6yr8nUnxXsFsRr8758XzvvIK3hfcpae5TVdZ1Pt40uvFx+nrz7RJv87DVVsV7Lb7nx2FmsrB1iazd35k/A58q7DoXbypdFb/fKb7EYYYuv/Dim6lUr/UCPd2ZV+9WK6+ewWzzeBPpYqOc9ZbYpR6Mrrga3o8v9VvtW97nfTqd7uBWL6q06xy8yXQV1joWX5IuZRd7OLpqBl50BdML9NTPW3u7RxvSWlVx38l669LVMXyL7BYV3np4M1rrZ1v9Ia2qvO9EvKl0eUP8qYJd7PH4ujl4sVUI3qxWVd53Et50uoq7HLUgZpfcXcZXLnjb9Qe3qgp9J+BNpssdoLZHzU1SUnhr4EXWIXhzWlWFvrl4yS9BCZNQdhU1N0lR4RW8q/V3yp7xgRWW3nS5/F+tSR6il7SLdkaMhMBLbnzBi7a23DwMvFl0FXvBaUmw+KJ2SwsvNdZVX530bKu/tfHm0OXv0bjw4nppu3h31GAEb7P+1sWbR1fxl3QXjRbfwsIreNfrb028WXQT3khG3IV6Swuv4G3a36pvCWC9mXQVf8nYsn7xxe1WKLzFeBu+nU7P0v2RWQVva7owO4cvwy7RJTmiQrzbys4G1ARvHt2UQ88YulkvYZdReAXvulkcby5dlbIstvBUfMsLr+BdNwvjzaSbdMaPNNfrrVB4Be+6abv9PL3ZdFXSwuTSuvhy7FIrIjsihi54y7Ig3ly6qWWXs/hPlN06hVfwNs1iePPpqqSFeYu/5kwMRa6J0ZXgbRh3QN5H4+vhzaabdn0bk67ZZ8D1sn4LGJ3x8PZzigwziwStW8m2B3Q5fdoEbwFdlbY0c3Gz04B/DdaieIc5Rcy/YetWsukBffwPe1YAvzUrWu9SdBPtdsS0ZvS6OL3xdxvOj/O/YesWsvEBNcCbTzf1ivhku+i0ZkvjvdzN/4atm8jGB1Qdbwldlbo88wHOgQboW9xKP/c7rwlptDbv0938b9i6jWx8QHXxfvfdd/lzPqnExfPsdvFvcVsabz+nSP9v2LqVbHxANfH2RTdTb0bZ5T4iOMIbFt96dvFnMm3efk6RYWaRoHUr2dmA8oc77i/k4VWpy/Oxx85OBN9BuDTejNYVsrMBWa1Jl5bOu7o5eFPLbqldv/gyyzi4DHtTCd6y8PHyV2O/S8vAq5IfUGq3c4ovs/AieNGHCd5qqb+h3QMMyXiTy24Vu+5XaBZOtyB4F0rtDR0cG0vUq9IWT3qrRlxKNs8pWVZ4Be9SqbuhI4d1k/BmlV3+Y4hLyfriW1x4Be9Sqbmho2ckEvCm003ZZaAv4TV8uYVX8K6fehsaOJnGx6vYS84PqWu3098Ay10nvJTgXSi1NjR4HpiLN6PsNrDLL7yCd/2039A8vYq1lPeY+nb5+9DIUoJ3obQ/oM7Bm1N20+ymFF7qUxb9knBTmxM/62dzA2KnJV6VNpT+MS3sjmtl6EU631lBZeeoIy/Bm1t2Ux6WYNesli6+SO+Cd2tphlclD6VL3WXg2rV/JSi9SP+Cd2uZR26+PD7hw4Ko3qyy29LutGK8+GL9W5fpDt/VfnqMtO4uBxh5/+XxCR8WxPCqrLEk2s0pvDqYXmwA9qbqP1e55peu1ssxRj68FsiHBYn30cPieWW3qV1nzWPx5T2bKc5ts5EE77qxRj58eTz2YUHieZrmfLppD+Taja2558t5NsBts5GerM9HHIPAzuKWk3viw4KMl1vljaOt3XDVWm8+3nEjnTf86R52DjDy/svjiQ8Lki93ZtlN3mXg24V+La7FNxfv8F3t94J35ThHG+464sOC1MutMkeRbLe08Or8lIt3+q7205anY2DnqCPP2efNSEO72P5IwT5v8so2nKOOfBm8re1Caxe8Jkcd+RJ4k9+qpdhF1y54TY468gXwtrcLrl7wmhx15BXwEicC0ulCdtMvRBS8JkcdeQ28+CMyjq1BePGOkh8heDef1fHia4wE2mkQvJk56sjb48VXGAm4wyt4M3PUkcOv33A9oPttF7XwJl4xk9vRfN90JegZuVpB8G4tmXiH6wG9b7uohhd9TNaD8KGNV4JesEttBO/Wkn9V4BWv/20Xu8Wrc37snr/+O4Y348/BHrLfkafFep799YDHwTtcjH+IixzTcpPPU+8fHgavvsjxrAvoEa4TS8vNPc/xesCD4J2uBJXKe9w4Rxv09YAHwTtdCSp4j5uFjvOu8oYttfkwkecJNgverUeeJ9jsn9d4On3yilphGd55WgWrJ8ELRp4n2Oyd17h89uZCzmpShrc/4/Dxr6+iraXdHC/yPMFm77zG+Z4x20H5bsP58cNfXlAfMRO8JvI8wWbvvMb50TlC0QjvtfhePv2Z+q51wWsizxNs9s5rpFXeYff17HxOl8Y7Tqtwwc84CF4TeZ5gs3deI22fd5oVzJ5AjRY/TasglZcReZ5gs39eI/low/nx/ENS5Z2nVSDOOAheE3meYHPpcd5r2TXXHfArb6WhyYt6sGRcJV6Id4RLn7fNwHvUixzTcivPMyNFeIfd10aVV2IimwZMEd5h9/Xs7L4K3rqRTQNmw9c2SExk04ARvFuPbBowgnfrkU0DRvBuPbJpwAjerUc2DRjBu/XIpgEjeLce2TRgcs5i5eGV02V5kU1TNXLRwZKRzVk1gnfJyOasGrliZsnI5pTsNoJXstsIXsluI3glu43glew2gley2wheyW4jeCW7jeCV7DaCV7LbCF7JbiN4JbuN4JXsNoJXstsIXsluI3glu43glew2gley2wheyW4jeCW7jeCV7DaCV7LbCF7JbiN4JbuN4JXsNoJXstsIXsluI3glu43glew2gley2wheyW4jeCW7jeCV7DaCV7Lb/H/ksTQkOqpxOQAAAABJRU5ErkJggg==" />
<!-- rnb-plot-end -->
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<!-- rnb-text-begin -->
## Network
<!-- rnb-text-end -->
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<!-- rnb-source-begin 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 -->
```r
library(EGAnet)
set.seed(12) #or 1
ega_60 <- ds_60_random %>% select(starts_with("q")) %>%
mutate_all(., ~case_when(. == "0" ~ 1,
. == "5" ~ 2,
. == "10" ~ 3)) %>%
EGA(.)Warning in EGA(.) :
Previous versions of EGAnet (<= 0.9.8) checked unidimensionality using uni.method = "expand" as the default
Exploratory Graph Analysis
• model = glasso
• algorithm = walktrap
• correlation = cor_auto
• unidimensional check = leading eigenvalue
Variables detected as ordinal: q_1; q_2; q_3; q_4; q_5; q_6; q_7; q_8; q_9; q_10; q_11; q_12; q_13; q_14; q_15; q_16; q_17; q_18; q_19; q_20; q_21; q_22; q_23; q_24; q_25; q_26; q_27; q_28; q_29; q_30; q_31; q_32
Warning in qgraph::cor_auto(data, forcePD = TRUE) :
Correlation matrix is not positive definite. Finding nearest positive definite matrix
ega_60
EGA Results:
Number of Dimensions:
[1] 6
Items per Dimension:```r
#methods.section(ega.wmt)
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<!-- rnb-text-begin -->
## Hull method
I need to export the dataset as CSV file and then run the analysis in Factor.
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```r
ds_60_random %>% select(starts_with("q")) %>%
mutate_all(., ~case_when(. == "0" ~ 1,
. == "5" ~ 2,
. == "10" ~ 3)) %>% write.csv(., "ds_60_random.csv", row.names = F)! Done.
If you use this syntax in your work, please cite it. Contact me at luisfca@puc-rio.br
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. https://creativecommons.org/licenses/by-nc-sa/4.0/
---
title: "R Notebook - Exploratory analysis - DA"
author: "Luis Anunciação"
output:
  html_notebook:
    toc: yes
    toc_float: yes
    number_sections: yes
    theme: united
    highlight: textmate
editor_options: 
  chunk_output_type: inline
---

<div class="alert alert-info">
**Note**: This is the R markdown of the manuscript "An Exploratory Analysis of the Internal Structure of Test Through a Multi-methods Exploratory Approach of the ASQ:SE in Brazil". The first set of chunks reproduce a previous published paper ("Confirmatory analysis and normative tables for the Brazilian
Ages and Stages Questionnaires: Social–Emotional") that used the same dataframe.

Click run to reproduce all analyzes.

If you have any questions or queries, please reach me out at luisfca@puc-rio.br

last updated: `r format(Sys.time(), '%d %B, %Y')`
</div>

# Main analysis

Last review on January 4, 2022.   

```{r}
load(url("https://osf.io/s8rxb/download"))
```

```{r}
#Packages
pacman::p_load(tidyverse, #enrironment
               arsenal,
               knitr,
               psych) #classical test
```


# Previous Wiley 

## Descriptives

Page 3

```{r}
ds_60 %>% 
  tableby(sex ~ score, data = .) %>% 
  summary()
```

## IRT

```{r}
cfa60 <- '
F1 = 2, 5, 6, 7, 9, 11, 12, 13, 15, 16, 17, 20, 22, 23, 24, 25, 26, 30, 31, 32
F2 = 1, 3, 4, 8, 10, 14, 18, 19, 21, 27, 28, 29
COV = F1*F2'
```

https://onlinelibrary.wiley.com/doi/10.1111/cch.12649     
Months 60   
M2 1,035.145 (current = 1053.881)   
df 431   
P <0.001   
RMSEA 0.05   
SRMSR 0.08   
TLI 0.91 (0.93)  
CFI 0.92 (0.94)  

```{r}
mirt::mirt(ds_60_random[-c(1:4,37)] , 
     cfa60, 
     itemtype= 'graded', method = 'MHRM') %>% 
  mirt::M2(.)
```



# Descriptive results

## Participants

Page 2. Therefore, a total of 500 children were randomly selected for the analyses. The randomness processwas 
initiated in the fairsubset R package,17 with the seed defined at 15 and RNGversion set at 3.6. This subsample comprised 276 males
(55.2%) and 224 females (44.8%).

```{r, results='asis'}
ds_60_random %>% 
  mutate(sex = factor(sex)) %>% 
  tableby(~ sex, data = .) %>% summary()
```
## Mean score

Page 3. The mean score for these participants was 41 (standard
deviation = 6.4, range: 0–205).

```{r, results='asis'}
ds_60_random %>% 
  tableby(~ score, data = .) %>% summary()
```


Page 3. No difference was found between this score and the score that was obtained with the full data set (t 22829 = -0.982, p = 0.326).

```{r}
t.test(ds_60$score, ds_60_random$score, var.equal = T)
```



## ASQ Items

```{r, results='asis'}
ds_60_random %>% select(starts_with("q")) %>% 
  mutate_all(., ~as.factor(.)) %>% 
  tableby(~., data = .) %>% summary()
```

# Reliability

Page 3. Cronbach’s α for this interval was 0.86 (95% confidence
interval [CI]: 0.85–0.88), with an average interitem correlation
of 0.17 (95% CI: 0.15–0.19). This age interval is composed
of 32 items, in which respondents choose one option that
best aligns with a target behavior of the child.

```{r}
ds_60_random %>% select(starts_with("q"))%>% alpha()
```

# Items


Page 4. The distribution of ASQ:SE items was right-skewed, indicating
deviation fromnormality and that the items’meanswere
greater than the medians. Skews ranged from 0.87 to 6.04.
Kurtosis ranged from 0.81 to 37.29. The Kaiser–Meyer–
Olkin test result was 0.86.

```{r}
ds_60_random %>% select(starts_with("q")) %>% 
  mutate_all(., ~case_when(. == "0" ~ 1,
                           . == "5" ~ 2,
                           . == "10" ~ 3)) %>% 
  psych::describe() %>% DT::datatable(.) #they define kurtosis as 0

#psych::describe(rnorm(1000,0,10))
```

Page 9. First result

```{r}
ds_60_random %>% select(starts_with("q")) %>% 
  mutate_all(., ~case_when(. == "0" ~ 1,
                           . == "5" ~ 2,
                           . == "10" ~ 3)) %>% 
  pivot_longer(everything()) %>% 
  ggplot(., aes(as.numeric(value), fill = name)) +
  geom_density(alpha  = 0.3)
```


# Exploratory analysis 

Page 4. The Kaiser–Meyer–
Olkin test result was 0.86. The Bartlett test result was
4629.517 (df¼496, p<0.001).

## KMO


```{r}
ds_60_random %>% select(starts_with("q")) %>% 
  mutate_all(., ~case_when(. == "0" ~ 1,
                           . == "5" ~ 2,
                           . == "10" ~ 3)) %>% KMO()
```
## Bartlett

```{r}
ds_60_random %>% select(starts_with("q")) %>% 
  mutate_all(., ~case_when(. == "0" ~ 1,
                           . == "5" ~ 2,
                           . == "10" ~ 3)) %>% psych::cortest.bartlett()

```

## Decide how many factors will be retained

## Polychoric matrix as input


```{r}
RNGversion(3.6)
set.seed(3)

rho_60 <- ds_60_random %>% select(starts_with("q")) %>% 
  mutate_all(., ~case_when(. == "0" ~ 1,
                           . == "5" ~ 2,
                           . == "10" ~ 3)) %>% 
  polychoric(.)
```

## Get rho from the polychoric matrix


```{r}
rho_60 <- rho_60$rho 
```


## Parallel Analysis (polychoric)

The following parallel analysis will define an arbitrarily set of subjects

```{r parallel analysis with polychoric correlation }
parallel <- rho_60 %>%
  fa.parallel(.) #arbitrarily set
```
On the other hand, the following PA will use the full random dataset

```{r}
parallel_full <- rho_60 %>%
  fa.parallel(.,n.obs = 500)
```


Parallel Analysis using polychoric correlation as input  
PCA:  10.72  4.46  1.91  1.48  1.33  1.26  1.13  1.02  0.92
EFA: 10.13  3.70  1.22  0.73

Page 4. Polychoric correlations of the PCA results were 10.72, 4.46, and 1.91,
respectively. T

EFA outcomes were 10.13, 3.70, and 1.22 for
polychoric correlations and 6.12, 2.26, and 0.83 for Pearson
correlations.

```{r}
parallel_full
```
## Build dataset for parallel analysis results (Polychoric) 

```{r }
#build the table
obs <- data.frame(parallel$fa.values, parallel$pc.values)
obs$type <- c('Observed Data')
obs$num <- c(row.names(obs))
obs$num <- as.numeric(obs$num)
colnames(obs) <- c('eigenvalue_fa', 'eigenvalue_pca','type', 'num')

obs <- obs %>% 
  pivot_longer(-c(num, type)) %>% 
  mutate(name = str_remove(name,"eigenvalue_")) %>% 
  mutate(name = str_remove(name,"eigenvalue_")) %>% 
  mutate(name = toupper(name))
```


## Parallel Analysis (Pearson correlation)

If I want to use the raw data (instead of a polychoric matrix as input), the results become fuzzy. 7 factors and 3 were recommended. However, due to the ordinal nature of the responses, the use of a polychoric matrix is recommended.  

```{r parallel analysis with Pearson correlation }
parallel_raw <- ds_60_random %>% select(starts_with("q")) %>% 
                                           mutate_all(., ~case_when(. == "0" ~ 1,
                                                                    . == "5" ~ 2,
                                                                    . == "10" ~ 3)) %>%
  fa.parallel(., cor = "cor")
```


Page 4. Pearson eigenvalues
PCA: 6.83, 3.12, 1.60 1.38 1.37 1.21 1.15 1.074 0.987
EFA: 6.12, 2.26, 0.83

```{r}
parallel_raw
```

## Build dataset for parallel analysis results (Pearson) 

A better plot using the raw data as input

```{r }
#build the table
obs_raw <- data.frame(parallel_raw$fa.values, parallel_raw$pc.values)
obs_raw$type <- c('Observed Data')
obs_raw$num <- c(row.names(obs_raw))
obs_raw$num <- as.numeric(obs_raw$num)
colnames(obs_raw) <- c('eigenvalue_fa', 'eigenvalue_pca','type', 'num')

obs_raw <- obs_raw %>% 
  pivot_longer(-c(num, type)) %>% 
  mutate(name = str_remove(name,"eigenvalue_")) %>% 
  mutate(name = str_remove(name,"eigenvalue_")) %>% 
  mutate(name = toupper(name))
```

Plotting via ggplot2

```{r, eval = FALSE }
plot_scree_pearson <- ggplot(obs_raw, aes(x = num, y = value, color = name)) +
  geom_point(size=2) +
  geom_line() + 
  scale_y_continuous(name='Eigenvalue')+
  scale_x_continuous(name='Factor Number', breaks=min(obs$num):max(obs$num))+
  geom_hline(yintercept = 1, linetype = 'dashed') +
  labs(color = "Method") +
  ggtitle("Pearson correlation") +
  theme_classic()
```


## Plot the scree plot via Parallel Analsysis

```{r}
data_plot_scree <- bind_rows(
obs_raw %>% 
  mutate(correlation = "Pearson")
  ,
obs %>% 
  mutate(correlation = "Polychoric")
) %>% 
  arrange(num)
```


```{r}
ggplot(data_plot_scree, aes(x = num, y = value,  shape = factor(correlation), linetype = factor(correlation), color = factor(name))) +
  geom_point(size=3) +
  geom_line(size=0.5) + 
  scale_y_continuous(name='Eigenvalue', breaks = 0:12)+
  scale_x_continuous(name='Factor Number', breaks=min(obs$num):max(obs$num))+
  geom_hline(yintercept = 1, linetype = 'dashed') +
  labs(color = "EFA or PCA", linetype = "Type of correlation", shape = "Type of correlation") +
  annotate(geom="text", x=28, y=1.5, label="Kaiser criterion")+
  geom_segment(aes(x = 3 , y=-Inf, xend = 3, yend = 7), linetype=2, color = "black")+
  annotate(geom="text", x=6, y=7, label="Elbow Rule")+
  theme_classic()
```


## Nest (Raw Data)

```{r}
source("C:/Users/luisf/Dropbox/Puc-Rio/Artigo - Theory and models/NEST.R")
```

```{r, eval = FALSE }
ds_60_random %>% select(starts_with("q")) %>% 
                                           mutate_all(., ~case_when(. == "0" ~ 1,
                                                                    . == "5" ~ 2,
                                                                    . == "10" ~ 3)) %>%
  NEST(.)
```


# Solutions


```{r function }
fatores_itens <- function(...) {
  j <- unclass(...$loadings) %>% #get vector
    as.data.frame() %>%  #transform into dataframe
    rownames_to_column("item") %>%  #assign a consistent name
    mutate(lambda = pmap_chr(select(., -c(item)), ~ if_else(abs(c(...)) %>% 
                                                              max  >= 0.3,"in","out")))  %>% 
    filter(lambda == "in") %>% #exclusion criteria (factor loadings)
    mutate(main_factor = pmap_chr(select(., -c(item, lambda)), ~ abs(c(...)) %>% 
                                    which.max %>% 
                                    names)) %>%  #return the items
    #return the items
    group_by(main_factor) %>% 
    mutate(itens_factor = paste0(item, collapse = ",")) %>% #insert y
    select(main_factor, itens_factor) %>% #select final results
    distinct(main_factor, .keep_all = TRUE) %>% #remove duplicates
    arrange(main_factor) %>% #to become easy to understand
    mutate(itens_factor = str_remove_all(string = itens_factor, pattern = "q_")) %>% #compile a better report
    mutate(numero = str_count(itens_factor, "\\d+")) %>% #count how many non-exclusive items
    janitor::adorn_totals()

  return(j)
}

```


## Solution: Elbow (Polychoric)

```{r sol elbow polychoric }
sol_elbow <- fa(rho_60,
   fm = "wls",
   nfactors = 2, rotate = "Promax")
```

```{r sol elbow display poly }
sol_elbow
```

```{r sol elbow main factor items poly }
fatores_itens(sol_elbow)
```

## Solution: Elbow (Pearson)

```{r sol elbow pearson }
sol_elbow_raw <- ds_60_random %>% select(starts_with("q")) %>% 
  mutate_all(., ~case_when(. == "0" ~ 1,
                           . == "5" ~ 2,
                           . == "10" ~ 3)) %>% 
  fa(.,
     fm = "wls",
     nfactors = 2, 
     rotate = "Promax")
```

```{r sol elbow display pearson }
sol_elbow_raw
```

```{r sol elbow main factor items pearson }
fatores_itens(sol_elbow_raw)
```

```{r graph sol elbow }
qgraph::qgraph.loadings(sol_elbow$loadings, 
                        model = "reflective",
                        posCol="blue",negCol="purple",
                        layout="circle",
                        width=20, minimum = 0.3,
                        title = "Exploratory Factor Analysis (Elbow method)")
```


## Solution: Parallel (Polychoric)

```{r sol paralel polychoric }
sol_parallel <- fa(rho_60,
                   fm = "wls",
                    nfactors = 3, #using the specific set of subjects
                   rotate = "Promax")
```

```{r}
sol_parallel
```

```{r}
fatores_itens(sol_parallel)
```



## Solution: Parallel (Pearson)

```{r sol paralel pearson }
sol_parallel_raw <- ds_60_random %>% select(starts_with("q")) %>% 
  mutate_all(., ~case_when(. == "0" ~ 1,
                           . == "5" ~ 2,
                           . == "10" ~ 3)) %>% 
  fa(.,
     fm = "wls",
     nfactors = 3, 
     rotate = "Promax")
```


```{r}
sol_parallel_raw
```


```{r}
fatores_itens(sol_parallel_raw)
```



```{r}
#library(semPlot)
#semPaths(semPlotModel(sol_parallel$loadings), 
#         layout="circle",
#         nCharNodes = 6)
qgraph::qgraph.loadings(sol_parallel$loadings, 
                        model = "reflective",
                        posCol="blue",negCol="purple",
                        layout="circle",
                        width=20,minimum = 0.3,
                        title = "Exploratory Factor Analysis (Parallel Analysis)")
```


## SOL PCA (Polychoric and Varimax)

```{r sol PCA poly }
sol_pca <- principal(rho_60,
                     nfactors = 2, rotate = "varimax")
sol_pca
```


## SOL PCA (Pearson)


```{r sol PCA pearson  }
sol_pca_raw <- ds_60_random %>% 
  select(starts_with("q")) %>% 
  mutate_all(., ~case_when(. == "0" ~ 1,
                           . == "5" ~ 2,
                           . == "10" ~ 3)) %>% 
  principal(.,
            nfactors = 2, rotate = "varimax")
sol_pca_raw
```



```{r}
qgraph::qgraph.loadings(sol_pca$loadings, 
                        model = "formative",
                        posCol="blue",negCol="purple",
                        layout="circle",
                        width=20,minimum = 0.3,
                        title = "Principal Component Analysis (Parallel Analysis)")
```


## Network

```{r}
library(EGAnet)
set.seed(12) #or 1
ega_60 <- ds_60_random %>% select(starts_with("q")) %>% 
                                           mutate_all(., ~case_when(. == "0" ~ 1,
                                                                    . == "5" ~ 2,
                                                                    . == "10" ~ 3)) %>% 
 
  EGA(.)
```

```{r}
ega_60
```


```{r}
methods.section(ega.wmt)
```



## Hull method

I need to export the dataset as CSV file and then run the analysis in Factor.

```{r, eval=FALSE }
ds_60_random %>% select(starts_with("q")) %>% 
                                           mutate_all(., ~case_when(. == "0" ~ 1,
                                                                    . == "5" ~ 2,
                                                                    . == "10" ~ 3)) %>% write.csv(., "ds_60_random.csv", row.names = F)
```


! Done.

If you use this syntax in your work, please cite it. 
Contact me at luisfca@puc-rio.br   
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. https://creativecommons.org/licenses/by-nc-sa/4.0/




