CFA-Cattell-Assignment
Reem Alshehri
2023-05-02
Part 1 -Basics:
#Part 1 -Basics
library(lavaan)## Warning: package 'lavaan' was built under R version 4.2.3## This is lavaan 0.6-15
## lavaan is FREE software! Please report any bugs.dat <- read.csv("cattell_open_psych_ger.csv")
colnames(dat) # variable names## [1] "A1" "A2" "A3" "A4" "A5" "A6" "A7" "A8" "A9" "A10" "B1" "B2"
## [13] "B3" "B4" "B5" "B6" "B7" "B8" "B9" "B10" "B11" "B12" "B13" "C1"
## [25] "C2" "C3" "C4" "C5" "C6" "C7" "C8" "C9" "C10" "D1" "D2" "D3"
## [37] "D4" "D5" "D6" "D7" "D8" "D9" "D10" "E1" "E2" "E3" "E4" "E5"
## [49] "E6" "E7" "E8" "E9" "E10" "F1" "F2" "F3" "F4" "F5" "F6" "F7"
## [61] "F8" "F9" "F10" "G1" "G2" "G3" "G4" "G5" "G6" "G7" "G8" "G9"
## [73] "G10" "H1" "H2" "H3" "H4" "H5" "H6" "H7" "H8" "H9" "H10" "I1"
## [85] "I2" "I3" "I4" "I5" "I6" "I7" "I8" "I9" "I10" "J1" "J2" "J3"
## [97] "J4" "J5" "J6" "J7" "J8" "J9" "J10" "K1" "K2" "K3" "K4" "K5"
## [109] "K6" "K7" "K8" "K9" "K10" "L1" "L2" "L3" "L4" "L5" "L6" "L7"
## [121] "L8" "L9" "L10" "M1" "M2" "M3" "M4" "M5" "M6" "M7" "M8" "M9"
## [133] "M10" "N1" "N2" "N3" "N4" "N5" "N6" "N7" "N8" "N9" "N10" "O1"
## [145] "O2" "O3" "O4" "O5" "O6" "O7" "O8" "O9" "O10" "P1" "P2" "P3"
## [157] "P4" "P5" "P6" "P7" "P8" "P9" "P10"#
library(psych)## Warning: package 'psych' was built under R version 4.2.2##
## Attaching package: 'psych'## The following object is masked from 'package:lavaan':
##
## cor2covdescribe(dat)## vars n mean sd median trimmed mad min max range skew kurtosis se
## A1 1 357 3.45 1.08 4 3.50 1.48 1 5 4 -0.57 -0.48 0.06
## A2 2 355 3.52 1.05 4 3.58 1.48 1 5 4 -0.57 -0.19 0.06
## A3 3 356 3.60 1.13 4 3.69 1.48 1 5 4 -0.71 -0.29 0.06
## A4 4 356 3.59 1.02 4 3.67 0.00 1 5 4 -0.83 0.16 0.05
## A5 5 355 3.62 0.96 4 3.69 1.48 1 5 4 -0.73 0.21 0.05
## A6 6 353 3.48 0.89 4 3.51 1.48 1 5 4 -0.34 0.10 0.05
## A7 7 355 3.67 1.00 4 3.76 0.00 1 5 4 -0.88 0.40 0.05
## A8 8 356 2.91 1.04 3 2.87 1.48 1 5 4 0.24 -0.82 0.06
## A9 9 357 2.24 1.08 2 2.14 1.48 1 5 4 0.75 -0.16 0.06
## A10 10 353 2.56 1.04 2 2.53 1.48 1 5 4 0.39 -0.51 0.06
## B1 11 357 3.76 0.86 4 3.83 0.00 1 5 4 -0.62 0.21 0.05
## B2 12 357 3.75 0.95 4 3.83 1.48 1 5 4 -0.67 0.12 0.05
## B3 13 356 4.33 0.72 4 4.44 1.48 2 5 3 -0.98 0.95 0.04
## B4 14 357 4.48 0.64 5 4.56 0.00 1 5 4 -1.09 1.63 0.03
## B5 15 354 4.13 0.83 4 4.23 1.48 1 5 4 -0.96 1.11 0.04
## B6 16 353 3.78 0.91 4 3.86 1.48 1 5 4 -0.57 -0.01 0.05
## B7 17 357 3.82 0.95 4 3.92 1.48 1 5 4 -0.81 0.36 0.05
## B8 18 356 3.95 0.93 4 4.05 1.48 1 5 4 -0.87 0.68 0.05
## B9 19 356 2.56 1.15 2 2.51 1.48 1 5 4 0.43 -0.86 0.06
## B10 20 356 2.44 1.02 2 2.39 1.48 1 5 4 0.54 -0.36 0.05
## B11 21 356 2.65 1.20 2 2.58 1.48 1 5 4 0.43 -0.80 0.06
## B12 22 357 1.71 0.83 2 1.57 1.48 1 5 4 1.31 1.85 0.04
## B13 23 357 1.91 1.02 2 1.75 1.48 1 5 4 0.99 0.16 0.05
## C1 24 356 2.90 1.17 3 2.89 1.48 1 5 4 0.04 -0.92 0.06
## C2 25 356 3.59 1.13 4 3.68 1.48 1 5 4 -0.61 -0.42 0.06
## C3 26 353 3.25 0.98 3 3.27 1.48 1 5 4 -0.26 -0.48 0.05
## C4 27 357 3.34 1.05 4 3.35 1.48 1 5 4 -0.30 -0.71 0.06
## C5 28 358 3.24 1.15 3 3.25 1.48 1 5 4 -0.18 -0.98 0.06
## C6 29 355 2.81 1.26 3 2.76 1.48 1 5 4 0.15 -1.13 0.07
## C7 30 357 2.82 1.22 3 2.78 1.48 1 5 4 0.16 -1.01 0.06
## C8 31 358 2.35 1.23 2 2.24 1.48 1 5 4 0.55 -0.79 0.07
## C9 32 355 2.45 1.24 2 2.34 1.48 1 5 4 0.50 -0.81 0.07
## C10 33 356 2.46 1.05 2 2.42 1.48 1 5 4 0.44 -0.63 0.06
## D1 34 356 3.48 1.00 4 3.51 1.48 1 5 4 -0.44 -0.43 0.05
## D2 35 356 3.31 1.06 3 3.31 1.48 1 5 4 -0.29 -0.73 0.06
## D3 36 355 3.53 1.04 4 3.58 1.48 1 5 4 -0.45 -0.48 0.06
## D4 37 355 3.70 1.03 4 3.77 1.48 1 5 4 -0.60 -0.46 0.05
## D5 38 357 3.56 0.96 4 3.62 1.48 1 5 4 -0.68 0.06 0.05
## D6 39 355 3.50 0.92 4 3.52 1.48 1 5 4 -0.39 -0.30 0.05
## D7 40 354 2.61 1.09 2 2.60 1.48 1 5 4 0.26 -0.93 0.06
## D8 41 356 2.01 0.84 2 1.92 0.00 1 5 4 0.83 0.68 0.04
## D9 42 358 2.67 0.98 3 2.69 1.48 1 5 4 0.14 -0.78 0.05
## D10 43 356 2.37 1.09 2 2.32 1.48 1 5 4 0.38 -0.93 0.06
## E1 44 357 2.25 1.06 2 2.17 1.48 1 5 4 0.42 -0.71 0.06
## E2 45 356 2.64 1.24 3 2.60 1.48 1 5 4 0.14 -1.13 0.07
## E3 46 356 3.56 1.04 4 3.62 1.48 1 5 4 -0.50 -0.46 0.06
## E4 47 357 2.48 1.16 2 2.42 1.48 1 5 4 0.37 -0.86 0.06
## E5 48 356 3.76 0.85 4 3.83 0.00 1 5 4 -0.83 0.81 0.04
## E6 49 357 2.55 1.17 2 2.49 1.48 1 5 4 0.38 -0.77 0.06
## E7 50 356 2.23 1.01 2 2.15 1.48 1 5 4 0.68 -0.30 0.05
## E8 51 356 3.31 1.21 3 3.35 1.48 1 5 4 -0.17 -1.04 0.06
## E9 52 355 2.03 0.97 2 1.89 1.48 1 5 4 1.05 0.92 0.05
## E10 53 357 2.43 1.17 2 2.32 1.48 1 5 4 0.61 -0.48 0.06
## F1 54 357 2.84 1.07 3 2.87 1.48 1 5 4 -0.05 -0.76 0.06
## F2 55 357 3.37 1.03 4 3.39 1.48 1 5 4 -0.49 -0.51 0.05
## F3 56 356 1.78 1.18 1 1.54 0.00 1 5 4 1.39 0.80 0.06
## F4 57 357 3.29 1.12 4 3.30 1.48 1 5 4 -0.29 -0.89 0.06
## F5 58 355 2.41 1.32 2 2.28 1.48 1 5 4 0.46 -0.99 0.07
## F6 59 356 2.85 1.05 3 2.87 1.48 1 5 4 0.07 -0.75 0.06
## F7 60 355 3.02 1.13 3 3.07 1.48 1 5 4 -0.23 -0.98 0.06
## F8 61 357 3.40 1.20 4 3.49 1.48 1 5 4 -0.55 -0.69 0.06
## F9 62 357 2.85 1.07 3 2.85 1.48 1 5 4 0.15 -0.77 0.06
## F10 63 357 3.19 1.04 3 3.22 1.48 1 5 4 -0.29 -0.69 0.05
## G1 64 357 3.31 1.05 3 3.34 1.48 1 5 4 -0.46 -0.43 0.06
## G2 65 357 2.74 1.21 3 2.71 1.48 1 5 4 0.13 -1.12 0.06
## G3 66 356 3.08 1.19 3 3.10 1.48 1 5 4 -0.13 -0.92 0.06
## G4 67 357 3.01 1.23 3 3.02 1.48 1 5 4 -0.13 -1.07 0.06
## G5 68 357 3.27 1.14 4 3.31 1.48 1 5 4 -0.37 -0.85 0.06
## G6 69 355 3.01 1.23 3 3.01 1.48 1 5 4 0.00 -1.06 0.07
## G7 70 357 2.85 1.21 3 2.82 1.48 1 5 4 0.13 -1.02 0.06
## G8 71 357 2.31 1.11 2 2.21 1.48 1 5 4 0.78 -0.21 0.06
## G9 72 357 3.41 1.17 4 3.46 1.48 1 5 4 -0.35 -0.90 0.06
## G10 73 356 3.18 1.12 3 3.16 1.48 1 5 4 0.01 -0.94 0.06
## H1 74 355 4.20 0.86 4 4.33 1.48 1 5 4 -1.06 0.72 0.05
## H2 75 356 4.02 0.97 4 4.15 1.48 1 5 4 -0.94 0.45 0.05
## H3 76 357 3.97 0.98 4 4.09 1.48 1 5 4 -0.66 -0.50 0.05
## H4 77 356 2.43 1.18 2 2.34 1.48 1 5 4 0.55 -0.68 0.06
## H5 78 357 3.04 1.30 3 3.06 1.48 1 5 4 -0.17 -1.17 0.07
## H6 79 357 3.51 1.07 4 3.57 1.48 1 5 4 -0.43 -0.44 0.06
## H7 80 357 2.79 1.32 2 2.74 1.48 1 5 4 0.27 -1.16 0.07
## H8 81 357 2.43 1.16 2 2.32 1.48 1 5 4 0.66 -0.35 0.06
## H9 82 355 1.91 1.00 2 1.74 1.48 1 5 4 1.04 0.40 0.05
## H10 83 356 2.50 1.14 2 2.42 1.48 1 5 4 0.64 -0.49 0.06
## I1 84 357 2.64 1.14 2 2.60 1.48 1 5 4 0.45 -0.75 0.06
## I2 85 356 3.37 1.09 4 3.40 1.48 1 5 4 -0.33 -0.79 0.06
## I3 86 354 3.13 1.04 3 3.15 1.48 1 5 4 -0.21 -0.71 0.06
## I4 87 357 2.91 1.14 3 2.90 1.48 1 5 4 0.14 -0.82 0.06
## I5 88 355 3.49 1.12 4 3.54 1.48 1 5 4 -0.47 -0.70 0.06
## I6 89 356 2.14 1.11 2 2.00 1.48 1 5 4 0.81 -0.12 0.06
## I7 90 356 2.99 1.02 3 3.06 1.48 1 5 4 -0.30 -0.67 0.05
## I8 91 358 3.28 1.10 4 3.32 1.48 1 5 4 -0.47 -0.62 0.06
## I9 92 356 3.29 0.98 3 3.36 1.48 1 5 4 -0.60 -0.13 0.05
## I10 93 355 3.23 1.08 3 3.28 1.48 1 5 4 -0.44 -0.60 0.06
## J1 94 356 3.73 1.05 4 3.82 1.48 1 5 4 -0.77 -0.09 0.06
## J2 95 357 3.82 1.14 4 3.95 1.48 1 5 4 -0.76 -0.35 0.06
## J3 96 355 3.66 1.13 4 3.75 1.48 1 5 4 -0.63 -0.43 0.06
## J4 97 357 3.76 1.11 4 3.87 1.48 1 5 4 -0.61 -0.50 0.06
## J5 98 355 3.52 0.98 4 3.55 1.48 1 5 4 -0.34 -0.35 0.05
## J6 99 357 3.31 1.03 3 3.33 1.48 1 5 4 -0.30 -0.38 0.05
## J7 100 356 3.36 1.05 4 3.38 1.48 1 5 4 -0.31 -0.67 0.06
## J8 101 356 2.72 1.03 3 2.74 1.48 1 5 4 0.14 -0.83 0.05
## J9 102 356 2.45 1.19 2 2.37 1.48 1 5 4 0.48 -0.86 0.06
## J10 103 355 2.34 1.13 2 2.25 1.48 1 5 4 0.61 -0.56 0.06
## K1 104 356 3.21 1.16 3 3.22 1.48 1 5 4 -0.13 -1.01 0.06
## K2 105 356 3.26 1.21 3 3.30 1.48 1 5 4 -0.18 -1.04 0.06
## K3 106 355 2.90 1.22 3 2.87 1.48 1 5 4 0.12 -1.05 0.06
## K4 107 356 3.16 1.17 3 3.18 1.48 1 5 4 -0.16 -0.98 0.06
## K5 108 355 3.16 1.12 3 3.13 1.48 1 5 4 0.02 -1.03 0.06
## K6 109 356 3.04 1.20 3 3.06 1.48 1 5 4 -0.19 -1.06 0.06
## K7 110 355 2.89 1.18 3 2.92 1.48 1 5 4 -0.12 -1.11 0.06
## K8 111 355 2.76 1.17 3 2.76 1.48 1 5 4 0.04 -1.07 0.06
## K9 112 356 2.89 1.21 3 2.91 1.48 1 5 4 -0.14 -1.19 0.06
## K10 113 356 3.50 1.11 4 3.57 1.48 1 5 4 -0.57 -0.49 0.06
## L1 114 355 3.24 1.28 4 3.30 1.48 1 5 4 -0.30 -1.10 0.07
## L2 115 353 2.67 1.14 2 2.64 1.48 1 5 4 0.31 -0.90 0.06
## L3 116 355 2.95 1.17 3 2.97 1.48 1 5 4 -0.03 -1.12 0.06
## L4 117 357 3.68 1.05 4 3.76 1.48 1 5 4 -0.64 -0.30 0.06
## L5 118 357 3.64 1.06 4 3.71 1.48 1 5 4 -0.64 -0.37 0.06
## L6 119 357 2.94 1.21 3 2.94 1.48 1 5 4 -0.05 -1.12 0.06
## L7 120 356 2.95 1.11 3 2.94 1.48 1 5 4 0.09 -0.96 0.06
## L8 121 354 2.68 1.16 2 2.65 1.48 1 5 4 0.31 -0.97 0.06
## L9 122 357 3.06 1.07 3 3.06 1.48 1 5 4 -0.07 -1.00 0.06
## L10 123 355 3.43 1.09 4 3.46 1.48 1 5 4 -0.37 -0.68 0.06
## M1 124 357 3.76 1.12 4 3.89 1.48 1 5 4 -0.83 -0.06 0.06
## M2 125 356 3.94 0.87 4 4.02 1.48 1 5 4 -0.84 0.84 0.05
## M3 126 357 4.33 0.71 4 4.44 1.48 2 5 3 -0.95 0.90 0.04
## M4 127 357 3.66 0.87 4 3.71 1.48 1 5 4 -0.41 -0.14 0.05
## M5 128 357 3.61 1.08 4 3.68 1.48 1 5 4 -0.49 -0.53 0.06
## M6 129 357 1.94 1.02 2 1.78 1.48 1 5 4 1.08 0.60 0.05
## M7 130 356 1.99 1.05 2 1.83 1.48 1 5 4 1.10 0.55 0.06
## M8 131 355 1.94 0.99 2 1.79 1.48 1 5 4 1.11 0.86 0.05
## M9 132 353 1.97 0.93 2 1.84 1.48 1 5 4 0.99 0.72 0.05
## M10 133 356 2.11 0.95 2 2.00 1.48 1 5 4 0.80 0.39 0.05
## N1 134 354 2.71 1.19 2 2.67 1.48 1 5 4 0.30 -0.93 0.06
## N2 135 357 3.75 0.98 4 3.82 1.48 1 5 4 -0.56 -0.37 0.05
## N3 136 356 4.01 0.85 4 4.09 1.48 1 5 4 -0.76 0.46 0.04
## N4 137 356 3.37 1.02 3 3.36 1.48 1 5 4 -0.11 -0.72 0.05
## N5 138 357 3.83 1.15 4 3.96 1.48 1 5 4 -0.84 -0.24 0.06
## N6 139 357 3.79 1.05 4 3.89 1.48 1 5 4 -0.68 -0.22 0.06
## N7 140 356 4.18 0.79 4 4.28 1.48 1 5 4 -0.97 1.22 0.04
## N8 141 355 3.48 0.99 4 3.54 1.48 1 5 4 -0.68 0.04 0.05
## N9 142 357 3.29 1.13 4 3.34 1.48 1 5 4 -0.42 -0.70 0.06
## N10 143 358 2.41 1.14 2 2.34 1.48 1 5 4 0.47 -0.71 0.06
## O1 144 356 3.44 1.04 4 3.47 1.48 1 5 4 -0.45 -0.55 0.06
## O2 145 354 2.71 1.18 3 2.69 1.48 1 5 4 0.12 -0.98 0.06
## O3 146 354 3.42 1.00 4 3.45 1.48 1 5 4 -0.56 -0.21 0.05
## O4 147 356 3.52 1.09 4 3.58 1.48 1 5 4 -0.53 -0.52 0.06
## O5 148 357 3.62 1.02 4 3.69 1.48 1 5 4 -0.53 -0.21 0.05
## O6 149 355 3.19 1.09 3 3.17 1.48 1 5 4 -0.13 -1.03 0.06
## O7 150 357 3.15 1.13 3 3.14 1.48 1 5 4 -0.08 -1.03 0.06
## O8 151 356 3.14 1.28 3 3.17 1.48 1 5 4 -0.13 -1.19 0.07
## O9 152 354 2.99 1.20 3 3.00 1.48 1 5 4 -0.06 -1.08 0.06
## O10 153 357 3.24 1.11 3 3.24 1.48 1 5 4 -0.22 -0.92 0.06
## P1 154 356 2.62 1.15 2 2.58 1.48 1 5 4 0.34 -0.91 0.06
## P2 155 357 2.41 1.17 2 2.33 1.48 1 5 4 0.51 -0.73 0.06
## P3 156 357 3.06 1.10 3 3.07 1.48 1 5 4 -0.08 -0.93 0.06
## P4 157 356 3.15 1.12 3 3.16 1.48 1 5 4 -0.19 -0.95 0.06
## P5 158 353 2.60 0.94 3 2.59 1.48 1 5 4 0.31 -0.17 0.05
## P6 159 357 3.00 1.10 3 2.96 1.48 1 5 4 0.13 -0.80 0.06
## P7 160 357 2.79 1.11 3 2.82 1.48 1 5 4 -0.03 -0.99 0.06
## P8 161 356 3.26 1.14 3 3.27 1.48 1 5 4 -0.20 -1.03 0.06
## P9 162 358 3.70 1.07 4 3.80 1.48 1 5 4 -0.83 0.07 0.06
## P10 163 357 3.39 1.05 4 3.42 1.48 1 5 4 -0.37 -0.53 0.061.a) How many factors? Warmth, Dominance
1.b) How many items on each factor?
warmth has 10 factors(A1-A10) ,Dominance has 10 factors(D1-D10)
2.Count the number of unique elements in your variance covariance matrix of the data.
unique elements in the variance-covariance matrix= 20*(20+1)/2= 210
3.Count the number of parameters in your basic model.
20 factors loadings + 20 error variances+ 1 correlation between both factors=41 parameters
4.The model degrees of freedom (df) should be (2) – (3) above.
df = 210-41= 169
#Fit the CFA
cfa_syntax <- " Warmth =~ A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + A9 + A10
Dominance =~ D1 + D2 + D3 + D4 + D5 + D6 + D7 + D8 + D9 + D10"
cfa_fit <- cfa(cfa_syntax, data = dat, std.lv = TRUE)
summary(cfa_fit,standardize= TRUE, rsquare= TRUE)## lavaan 0.6.15 ended normally after 15 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 41
##
## Used Total
## Number of observations 328 358
##
## Model Test User Model:
##
## Test statistic 465.974
## Degrees of freedom 169
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Warmth =~
## A1 0.637 0.057 11.165 0.000 0.637 0.596
## A2 0.652 0.054 12.012 0.000 0.652 0.632
## A3 0.700 0.058 11.991 0.000 0.700 0.631
## A4 0.674 0.051 13.107 0.000 0.674 0.676
## A5 0.638 0.050 12.786 0.000 0.638 0.663
## A6 0.529 0.047 11.345 0.000 0.529 0.603
## A7 0.579 0.053 10.926 0.000 0.579 0.585
## A8 -0.586 0.056 -10.480 0.000 -0.586 -0.565
## A9 -0.827 0.053 -15.461 0.000 -0.827 -0.763
## A10 -0.384 0.059 -6.532 0.000 -0.384 -0.372
## Dominance =~
## D1 0.756 0.050 15.139 0.000 0.756 0.759
## D2 0.630 0.058 10.802 0.000 0.630 0.585
## D3 0.360 0.060 6.018 0.000 0.360 0.348
## D4 0.474 0.057 8.252 0.000 0.474 0.464
## D5 0.655 0.051 12.877 0.000 0.655 0.673
## D6 0.463 0.051 9.145 0.000 0.463 0.508
## D7 -0.779 0.056 -13.944 0.000 -0.779 -0.715
## D8 -0.348 0.047 -7.322 0.000 -0.348 -0.417
## D9 -0.602 0.052 -11.531 0.000 -0.602 -0.617
## D10 -0.577 0.060 -9.642 0.000 -0.577 -0.532
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Warmth ~~
## Dominance 0.264 0.060 4.379 0.000 0.264 0.264
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A1 0.739 0.063 11.746 0.000 0.739 0.645
## .A2 0.641 0.056 11.525 0.000 0.641 0.601
## .A3 0.741 0.064 11.531 0.000 0.741 0.602
## .A4 0.540 0.048 11.179 0.000 0.540 0.543
## .A5 0.518 0.046 11.289 0.000 0.518 0.560
## .A6 0.488 0.042 11.702 0.000 0.488 0.636
## .A7 0.643 0.054 11.803 0.000 0.643 0.658
## .A8 0.732 0.061 11.901 0.000 0.732 0.680
## .A9 0.490 0.048 10.101 0.000 0.490 0.417
## .A10 0.916 0.073 12.498 0.000 0.916 0.861
## .D1 0.420 0.043 9.751 0.000 0.420 0.424
## .D2 0.763 0.065 11.648 0.000 0.763 0.658
## .D3 0.943 0.075 12.501 0.000 0.943 0.879
## .D4 0.819 0.067 12.196 0.000 0.819 0.784
## .D5 0.520 0.047 10.955 0.000 0.520 0.547
## .D6 0.615 0.051 12.033 0.000 0.615 0.742
## .D7 0.582 0.056 10.463 0.000 0.582 0.489
## .D8 0.574 0.047 12.339 0.000 0.574 0.826
## .D9 0.590 0.052 11.436 0.000 0.590 0.620
## .D10 0.846 0.071 11.930 0.000 0.846 0.717
## Warmth 1.000 1.000 1.000
## Dominance 1.000 1.000 1.000
##
## R-Square:
## Estimate
## A1 0.355
## A2 0.399
## A3 0.398
## A4 0.457
## A5 0.440
## A6 0.364
## A7 0.342
## A8 0.320
## A9 0.583
## A10 0.139
## D1 0.576
## D2 0.342
## D3 0.121
## D4 0.216
## D5 0.453
## D6 0.258
## D7 0.511
## D8 0.174
## D9 0.380
## D10 0.283- Let’s examine the model parameters:
- Loadings: are they consistent with any theoretical expectations?
all factors are significant P<0.001 , negative loadings indicates to reverse coding in the survye items.
- Are there any marked differences between the unstandardized and standardized loadings?
there are slight differences between the unstandardized and standardized loadings.
- What proportion of variance is explained in the items by the factors?
we can conclude that from the R-Square which is between 12.1% and 58.3%: A1 0.355 A2 0.399 A3 0.398 A4 0.457 A5 0.440 A6 0.364 A7 0.342 A8 0.320 A9 0.583 A10 0.139 D1 0.576 D2 0.342 D3 0.121 D4 0.216 D5 0.453 D6 0.258 D7 0.511 D8 0.174 D9 0.380 D10 0.283
- If you have multiple factors, what is the correlation between your factors? If any two factors have a very high correlation, can you claim these factor to relate to different constructs? Might there be some justification to merge both these factors into one.
I have 2 factors (Warmth, Dominance ) and they are slightly low correlated 0.264
Part2:Experimentation
#Part2- Experimentation
cfa2_syntax <- "
Warmth =~ A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + A9 + A10
Dominance1 =~ D1 + D2 + D3 + D4 + D5
Dominance2=~ D6 + D7 + D8 + D9 + D10"
cfa2_fit <- cfa(cfa2_syntax, data = dat, std.lv = TRUE)
summary(cfa2_fit,standardize= TRUE, rsquare= TRUE)## lavaan 0.6.15 ended normally after 17 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 43
##
## Used Total
## Number of observations 328 358
##
## Model Test User Model:
##
## Test statistic 449.657
## Degrees of freedom 167
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Warmth =~
## A1 0.639 0.057 11.192 0.000 0.639 0.597
## A2 0.655 0.054 12.085 0.000 0.655 0.634
## A3 0.700 0.058 11.998 0.000 0.700 0.631
## A4 0.674 0.051 13.096 0.000 0.674 0.675
## A5 0.639 0.050 12.813 0.000 0.639 0.664
## A6 0.530 0.047 11.377 0.000 0.530 0.605
## A7 0.579 0.053 10.944 0.000 0.579 0.586
## A8 -0.582 0.056 -10.399 0.000 -0.582 -0.562
## A9 -0.826 0.053 -15.452 0.000 -0.826 -0.763
## A10 -0.379 0.059 -6.452 0.000 -0.379 -0.368
## Dominance1 =~
## D1 0.784 0.050 15.644 0.000 0.784 0.787
## D2 0.634 0.059 10.807 0.000 0.634 0.589
## D3 0.356 0.060 5.903 0.000 0.356 0.344
## D4 0.458 0.058 7.885 0.000 0.458 0.449
## D5 0.670 0.051 13.115 0.000 0.670 0.687
## Dominance2 =~
## D6 0.446 0.052 8.619 0.000 0.446 0.490
## D7 -0.820 0.057 -14.509 0.000 -0.820 -0.752
## D8 -0.346 0.048 -7.172 0.000 -0.346 -0.415
## D9 -0.642 0.052 -12.268 0.000 -0.642 -0.658
## D10 -0.605 0.060 -10.019 0.000 -0.605 -0.557
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Warmth ~~
## Dominance1 0.331 0.061 5.385 0.000 0.331 0.331
## Dominance2 0.177 0.067 2.651 0.008 0.177 0.177
## Dominance1 ~~
## Dominance2 0.905 0.033 27.341 0.000 0.905 0.905
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A1 0.738 0.063 11.747 0.000 0.738 0.644
## .A2 0.637 0.055 11.513 0.000 0.637 0.597
## .A3 0.741 0.064 11.537 0.000 0.741 0.602
## .A4 0.541 0.048 11.194 0.000 0.541 0.544
## .A5 0.517 0.046 11.290 0.000 0.517 0.559
## .A6 0.487 0.042 11.701 0.000 0.487 0.635
## .A7 0.642 0.054 11.805 0.000 0.642 0.657
## .A8 0.737 0.062 11.924 0.000 0.737 0.685
## .A9 0.491 0.048 10.125 0.000 0.491 0.418
## .A10 0.919 0.073 12.508 0.000 0.919 0.865
## .D1 0.377 0.044 8.612 0.000 0.377 0.380
## .D2 0.757 0.066 11.508 0.000 0.757 0.653
## .D3 0.946 0.076 12.484 0.000 0.946 0.882
## .D4 0.834 0.068 12.197 0.000 0.834 0.799
## .D5 0.501 0.047 10.574 0.000 0.501 0.527
## .D6 0.630 0.053 11.954 0.000 0.630 0.760
## .D7 0.517 0.057 9.105 0.000 0.517 0.435
## .D8 0.575 0.047 12.245 0.000 0.575 0.828
## .D9 0.539 0.050 10.689 0.000 0.539 0.567
## .D10 0.813 0.070 11.579 0.000 0.813 0.689
## Warmth 1.000 1.000 1.000
## Dominance1 1.000 1.000 1.000
## Dominance2 1.000 1.000 1.000
##
## R-Square:
## Estimate
## A1 0.356
## A2 0.403
## A3 0.398
## A4 0.456
## A5 0.441
## A6 0.365
## A7 0.343
## A8 0.315
## A9 0.582
## A10 0.135
## D1 0.620
## D2 0.347
## D3 0.118
## D4 0.201
## D5 0.473
## D6 0.240
## D7 0.565
## D8 0.172
## D9 0.433
## D10 0.311What is the correlation between the two new sub-factors? Any comments?
The new sub-factors Dominance1 and Dominance2 they are high correlated. Dominance1 ~~ Dominance2 = 0.905
Manual Calculation:
1.Use the unstandardized loadings and any other relevant parameters to compute the standardized loadings – verify the result is correct (3 items).
The standardized loading for items are: A2: \(\frac{0.652}{\sqrt{(0.652^2 +0.641)}}\) = 0.631
A8: \(\frac{ -0.586}{\sqrt{( -0.586)^2 + 0.732}}\) = -0.565
D1: \(\frac{0.756}{\sqrt{(0.756^2 + 0.420)}}\) = 0.759
2.Compute the proportion of variance explained in an item by the factor using the unstandardized estimates – verify the result is correct (3 items).
The variance is the square of standard deviation
- Use the standardized estimates to compute the model-implied correlation between 3 pairs of items.
A2 and A8 is: \(0.632 \times -0.565 =\) -0.357
A2 and D1 is: \(0.632 \times 0.759 \times 0.264 =\) 0.127
D1 and A8 is: $ 0.759 =$ -0.113
- Your result should match the model-implied correlation matrix from
lavaan. i.This syntax:
cov2cor(fitted([FITTED MODEL OBJECT])$cov)should return the model-implied correlation between your items.
lav_cor <- cov2cor(fitted(cfa_fit)$cov)
lav_cor["A2", "A8"]## [1] -0.357081lav_cor["A2", "D1"]## [1] 0.1268034lav_cor["D1", "A8"]## [1] -0.1135029- Compare the model-implied correlation to the sample correlation between the pair of items. In your opinion, does the model do a good job of matching the correlation between the pair of items?
I compare the same three sample correlations:
The model-implied and sample correlations are all close to each other for the three pairs I considered.
lavaan also returns the matrix of residual correlations:
resid(cfa_fit, type = "cor")$cov## A1 A2 A3 A4 A5 A6 A7 A8 A9 A10
## A1 0.000
## A2 0.001 0.000
## A3 0.108 -0.050 0.000
## A4 -0.053 -0.033 -0.057 0.000
## A5 0.060 0.082 -0.011 -0.112 0.000
## A6 0.178 0.131 -0.062 -0.088 0.167 0.000
## A7 -0.107 0.003 -0.020 0.043 0.020 -0.037 0.000
## A8 0.064 0.090 -0.013 -0.085 0.075 0.059 -0.119 0.000
## A9 0.082 0.024 -0.035 -0.139 0.047 0.109 0.009 0.047 0.000
## A10 0.028 0.051 -0.135 -0.012 0.071 0.087 0.016 0.006 0.046 0.000
## D1 0.130 0.091 0.050 0.064 0.106 0.053 0.079 0.021 -0.085 -0.038
## D2 0.075 0.061 -0.081 -0.045 0.024 -0.027 -0.057 0.116 0.031 0.008
## D3 0.021 0.084 0.021 0.058 0.033 0.029 0.049 0.045 -0.043 -0.044
## D4 -0.016 0.001 -0.110 -0.056 0.019 -0.069 -0.075 0.052 0.033 0.043
## D5 0.097 0.082 -0.060 -0.030 0.056 0.020 0.080 0.019 -0.031 -0.032
## D6 0.036 0.053 -0.010 -0.051 0.025 0.028 -0.022 0.135 0.059 -0.039
## D7 -0.051 0.025 0.059 0.020 -0.023 -0.041 -0.025 0.040 -0.031 0.097
## D8 0.005 -0.002 0.067 -0.013 0.001 0.100 0.002 0.032 0.087 0.160
## D9 0.018 0.081 0.103 0.081 0.036 0.151 0.053 -0.056 -0.059 0.050
## D10 -0.013 0.054 0.190 0.142 0.035 0.117 0.161 -0.104 -0.090 -0.015
## D1 D2 D3 D4 D5 D6 D7 D8 D9 D10
## A1
## A2
## A3
## A4
## A5
## A6
## A7
## A8
## A9
## A10
## D1 0.000
## D2 0.049 0.000
## D3 -0.032 -0.022 0.000
## D4 -0.068 -0.027 0.167 0.000
## D5 0.052 0.020 -0.056 -0.007 0.000
## D6 0.026 0.093 0.077 0.034 -0.015 0.000
## D7 0.031 0.045 0.009 -0.006 0.036 0.034 0.000
## D8 0.035 -0.017 -0.007 -0.064 0.002 -0.029 0.005 0.000
## D9 0.012 0.053 0.050 -0.026 0.043 0.086 0.129 -0.036 0.000
## D10 0.034 0.045 -0.052 -0.018 -0.016 0.048 0.039 0.019 0.052 0.000It’s difficult to look at all of this, so I try using a heatmap:
library(corrplot)## Warning: package 'corrplot' was built under R version 4.2.3## corrplot 0.92 loadedcorrplot(
resid(cfa_fit, type = "cor")$cov,
type = "lower", is.corr = FALSE
)
Part3:Model misspecification
There is some misspecification given the \(\chi^2\) test results, \(\chi^2(169) = 466,\ p < .001\). And the goodness of fit indices are larger than the guidelines suggest.
#Part3-misspecification
summary(cfa_fit, fit.measures = TRUE, estimates = FALSE)## lavaan 0.6.15 ended normally after 15 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 41
##
## Used Total
## Number of observations 328 358
##
## Model Test User Model:
##
## Test statistic 465.974
## Degrees of freedom 169
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 2206.555
## Degrees of freedom 190
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.853
## Tucker-Lewis Index (TLI) 0.834
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -8482.372
## Loglikelihood unrestricted model (H1) -8249.385
##
## Akaike (AIC) 17046.745
## Bayesian (BIC) 17202.258
## Sample-size adjusted Bayesian (SABIC) 17072.207
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.073
## 90 Percent confidence interval - lower 0.065
## 90 Percent confidence interval - upper 0.081
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.081
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.064# missing ML
cfa_fit <- cfa(cfa_syntax, data = dat, std.lv = TRUE, missing = "ML")
head(modificationIndices(cfa_fit, sort. = TRUE, power = TRUE))## lhs op rhs mi epc sepc.all delta ncp power decision
## 144 A4 ~~ A9 46.237 -0.235 -0.460 0.1 8.378 0.825 *epc:m*
## 90 A1 ~~ A6 34.428 0.204 0.348 0.1 8.303 0.822 *epc:m*
## 156 A5 ~~ A6 31.760 0.170 0.342 0.1 10.939 0.911 *epc:m*
## 271 D7 ~~ D9 26.327 0.199 0.326 0.1 6.638 0.731 **(m)**
## 173 A6 ~~ A9 25.823 0.158 0.333 0.1 10.303 0.894 *epc:m*
## 140 A4 ~~ A5 20.502 -0.151 -0.281 0.1 9.038 0.852 *epc:m*#Modification A4~~A9
cfa_syntax_mod <- " Warmth =~ A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + A9 + A10
Dominance =~ D1 + D2 + D3 + D4 + D5 + D6 + D7 + D8 + D9 + D10
A4~~A9
"
cfa_fit_mod <- cfa(cfa_syntax_mod, data = dat, std.lv = TRUE)
summary(cfa_fit_mod,standardize= TRUE, rsquare= TRUE)## lavaan 0.6.15 ended normally after 19 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 42
##
## Used Total
## Number of observations 328 358
##
## Model Test User Model:
##
## Test statistic 420.841
## Degrees of freedom 168
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Warmth =~
## A1 0.670 0.057 11.775 0.000 0.670 0.626
## A2 0.671 0.054 12.344 0.000 0.671 0.650
## A3 0.701 0.059 11.904 0.000 0.701 0.631
## A4 0.594 0.054 10.977 0.000 0.594 0.595
## A5 0.675 0.049 13.648 0.000 0.675 0.702
## A6 0.568 0.046 12.310 0.000 0.568 0.648
## A7 0.568 0.054 10.592 0.000 0.568 0.574
## A8 -0.557 0.057 -9.778 0.000 -0.557 -0.537
## A9 -0.758 0.056 -13.562 0.000 -0.758 -0.700
## A10 -0.369 0.059 -6.218 0.000 -0.369 -0.358
## Dominance =~
## D1 0.756 0.050 15.142 0.000 0.756 0.759
## D2 0.630 0.058 10.808 0.000 0.630 0.585
## D3 0.360 0.060 6.015 0.000 0.360 0.348
## D4 0.474 0.057 8.249 0.000 0.474 0.464
## D5 0.656 0.051 12.887 0.000 0.656 0.673
## D6 0.463 0.051 9.156 0.000 0.463 0.509
## D7 -0.780 0.056 -13.946 0.000 -0.780 -0.715
## D8 -0.347 0.047 -7.307 0.000 -0.347 -0.416
## D9 -0.601 0.052 -11.519 0.000 -0.601 -0.616
## D10 -0.577 0.060 -9.641 0.000 -0.577 -0.532
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A4 ~~
## .A9 -0.258 0.044 -5.837 0.000 -0.258 -0.415
## Warmth ~~
## Dominance 0.273 0.061 4.494 0.000 0.273 0.273
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A1 0.697 0.061 11.405 0.000 0.697 0.608
## .A2 0.616 0.055 11.216 0.000 0.616 0.578
## .A3 0.740 0.065 11.364 0.000 0.740 0.601
## .A4 0.642 0.056 11.494 0.000 0.642 0.646
## .A5 0.469 0.044 10.688 0.000 0.469 0.507
## .A6 0.445 0.040 11.228 0.000 0.445 0.580
## .A7 0.655 0.056 11.738 0.000 0.655 0.670
## .A8 0.765 0.064 11.927 0.000 0.765 0.711
## .A9 0.599 0.056 10.668 0.000 0.599 0.511
## .A10 0.927 0.074 12.488 0.000 0.927 0.872
## .D1 0.420 0.043 9.752 0.000 0.420 0.424
## .D2 0.762 0.065 11.647 0.000 0.762 0.658
## .D3 0.943 0.075 12.501 0.000 0.943 0.879
## .D4 0.819 0.067 12.197 0.000 0.819 0.785
## .D5 0.519 0.047 10.952 0.000 0.519 0.547
## .D6 0.615 0.051 12.031 0.000 0.615 0.741
## .D7 0.582 0.056 10.464 0.000 0.582 0.489
## .D8 0.574 0.047 12.342 0.000 0.574 0.827
## .D9 0.590 0.052 11.441 0.000 0.590 0.620
## .D10 0.846 0.071 11.930 0.000 0.846 0.717
## Warmth 1.000 1.000 1.000
## Dominance 1.000 1.000 1.000
##
## R-Square:
## Estimate
## A1 0.392
## A2 0.422
## A3 0.399
## A4 0.354
## A5 0.493
## A6 0.420
## A7 0.330
## A8 0.289
## A9 0.489
## A10 0.128
## D1 0.576
## D2 0.342
## D3 0.121
## D4 0.215
## D5 0.453
## D6 0.259
## D7 0.511
## D8 0.173
## D9 0.380
## D10 0.283#
cfa_fit_mod <- cfa(cfa_syntax_mod, data = dat, std.lv = TRUE, missing = "ML")
head(modificationIndices(cfa_fit_mod, sort. = TRUE, power = TRUE))## lhs op rhs mi epc sepc.all delta ncp power decision
## 271 D7 ~~ D9 26.451 0.200 0.326 0.1 6.637 0.731 **(m)**
## 91 A1 ~~ A6 24.971 0.170 0.311 0.1 8.689 0.838 *epc:m*
## 156 A5 ~~ A6 19.776 0.131 0.288 0.1 11.461 0.923 *epc:m*
## 248 D3 ~~ D4 17.301 0.204 0.230 0.1 4.177 0.533 **(m)**
## 92 A1 ~~ A7 16.554 -0.161 -0.245 0.1 6.408 0.716 **(m)**
## 185 A7 ~~ A8 14.676 -0.155 -0.224 0.1 6.083 0.694 **(m)**#Modification D7~~D9
cfa_syntax_mod <- " Warmth =~ A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + A9 + A10
Dominance =~ D1 + D2 + D3 + D4 + D5 + D6 + D7 + D8 + D9 + D10
A4~~A9
D7~~D9
"
cfa_fit_mod <- cfa(cfa_syntax_mod, data = dat, std.lv = TRUE)
summary(cfa_fit_mod,standardize= TRUE, rsquare= TRUE)## lavaan 0.6.15 ended normally after 20 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 43
##
## Used Total
## Number of observations 328 358
##
## Model Test User Model:
##
## Test statistic 394.746
## Degrees of freedom 167
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Warmth =~
## A1 0.670 0.057 11.783 0.000 0.670 0.626
## A2 0.672 0.054 12.361 0.000 0.672 0.650
## A3 0.700 0.059 11.897 0.000 0.700 0.631
## A4 0.594 0.054 10.973 0.000 0.594 0.595
## A5 0.675 0.049 13.656 0.000 0.675 0.702
## A6 0.568 0.046 12.316 0.000 0.568 0.649
## A7 0.568 0.054 10.589 0.000 0.568 0.574
## A8 -0.556 0.057 -9.760 0.000 -0.556 -0.536
## A9 -0.758 0.056 -13.562 0.000 -0.758 -0.700
## A10 -0.369 0.059 -6.211 0.000 -0.369 -0.358
## Dominance =~
## D1 0.770 0.050 15.383 0.000 0.770 0.773
## D2 0.645 0.058 11.053 0.000 0.645 0.599
## D3 0.365 0.060 6.058 0.000 0.365 0.352
## D4 0.470 0.058 8.116 0.000 0.470 0.460
## D5 0.669 0.051 13.122 0.000 0.669 0.686
## D6 0.476 0.051 9.400 0.000 0.476 0.523
## D7 -0.733 0.058 -12.736 0.000 -0.733 -0.672
## D8 -0.349 0.048 -7.319 0.000 -0.349 -0.419
## D9 -0.547 0.054 -10.109 0.000 -0.547 -0.561
## D10 -0.567 0.060 -9.376 0.000 -0.567 -0.522
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A4 ~~
## .A9 -0.258 0.044 -5.843 0.000 -0.258 -0.416
## .D7 ~~
## .D9 0.205 0.045 4.606 0.000 0.205 0.315
## Warmth ~~
## Dominance 0.286 0.061 4.718 0.000 0.286 0.286
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A1 0.696 0.061 11.405 0.000 0.696 0.608
## .A2 0.615 0.055 11.212 0.000 0.615 0.577
## .A3 0.741 0.065 11.369 0.000 0.741 0.602
## .A4 0.643 0.056 11.497 0.000 0.643 0.646
## .A5 0.469 0.044 10.688 0.000 0.469 0.507
## .A6 0.445 0.040 11.228 0.000 0.445 0.579
## .A7 0.656 0.056 11.740 0.000 0.656 0.670
## .A8 0.766 0.064 11.933 0.000 0.766 0.712
## .A9 0.599 0.056 10.672 0.000 0.599 0.511
## .A10 0.927 0.074 12.490 0.000 0.927 0.872
## .D1 0.399 0.043 9.195 0.000 0.399 0.402
## .D2 0.743 0.065 11.457 0.000 0.743 0.641
## .D3 0.939 0.075 12.468 0.000 0.939 0.876
## .D4 0.823 0.068 12.164 0.000 0.823 0.788
## .D5 0.502 0.047 10.643 0.000 0.502 0.529
## .D6 0.602 0.051 11.903 0.000 0.602 0.726
## .D7 0.652 0.061 10.738 0.000 0.652 0.548
## .D8 0.573 0.047 12.297 0.000 0.573 0.824
## .D9 0.652 0.056 11.577 0.000 0.652 0.685
## .D10 0.858 0.072 11.908 0.000 0.858 0.728
## Warmth 1.000 1.000 1.000
## Dominance 1.000 1.000 1.000
##
## R-Square:
## Estimate
## A1 0.392
## A2 0.423
## A3 0.398
## A4 0.354
## A5 0.493
## A6 0.421
## A7 0.330
## A8 0.288
## A9 0.489
## A10 0.128
## D1 0.598
## D2 0.359
## D3 0.124
## D4 0.212
## D5 0.471
## D6 0.274
## D7 0.452
## D8 0.176
## D9 0.315
## D10 0.272#
cfa_fit_mod <- cfa(cfa_syntax_mod, data = dat, std.lv = TRUE, missing = "ML")
head(modificationIndices(cfa_fit_mod, sort. = TRUE, power = TRUE))## lhs op rhs mi epc sepc.all delta ncp power decision
## 92 A1 ~~ A6 24.876 0.169 0.311 0.1 8.697 0.839 *epc:m*
## 157 A5 ~~ A6 19.683 0.131 0.287 0.1 11.473 0.923 *epc:m*
## 249 D3 ~~ D4 17.279 0.204 0.230 0.1 4.152 0.531 **(m)**
## 93 A1 ~~ A7 16.558 -0.161 -0.245 0.1 6.410 0.716 **(m)**
## 186 A7 ~~ A8 14.767 -0.156 -0.224 0.1 6.079 0.693 **(m)**
## 131 A3 ~~ A10 14.055 -0.179 -0.215 0.1 4.364 0.551 **(m)**#Modification A1~~A6
cfa_syntax_mod <- " Warmth =~ A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + A9 + A10
Dominance =~ D1 + D2 + D3 + D4 + D5 + D6 + D7 + D8 + D9 + D10
A4~~A9
D7~~D9
A1~~A6
"
cfa_fit_mod <- cfa(cfa_syntax_mod, data = dat, std.lv = TRUE)
summary(cfa_fit_mod,standardize= TRUE, rsquare= TRUE)## lavaan 0.6.15 ended normally after 20 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 44
##
## Used Total
## Number of observations 328 358
##
## Model Test User Model:
##
## Test statistic 372.855
## Degrees of freedom 166
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Warmth =~
## A1 0.625 0.058 10.698 0.000 0.625 0.584
## A2 0.665 0.055 12.137 0.000 0.665 0.644
## A3 0.707 0.059 11.971 0.000 0.707 0.637
## A4 0.612 0.054 11.301 0.000 0.612 0.614
## A5 0.660 0.050 13.193 0.000 0.660 0.687
## A6 0.529 0.047 11.161 0.000 0.529 0.604
## A7 0.586 0.054 10.942 0.000 0.586 0.592
## A8 -0.576 0.057 -10.122 0.000 -0.576 -0.555
## A9 -0.784 0.056 -14.107 0.000 -0.784 -0.724
## A10 -0.383 0.059 -6.440 0.000 -0.383 -0.372
## Dominance =~
## D1 0.770 0.050 15.378 0.000 0.770 0.773
## D2 0.645 0.058 11.047 0.000 0.645 0.599
## D3 0.365 0.060 6.060 0.000 0.365 0.352
## D4 0.470 0.058 8.120 0.000 0.470 0.460
## D5 0.669 0.051 13.118 0.000 0.669 0.686
## D6 0.476 0.051 9.393 0.000 0.476 0.523
## D7 -0.733 0.058 -12.734 0.000 -0.733 -0.672
## D8 -0.350 0.048 -7.331 0.000 -0.350 -0.420
## D9 -0.548 0.054 -10.120 0.000 -0.548 -0.561
## D10 -0.567 0.060 -9.375 0.000 -0.567 -0.522
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A4 ~~
## .A9 -0.228 0.043 -5.264 0.000 -0.228 -0.387
## .D7 ~~
## .D9 0.205 0.045 4.599 0.000 0.205 0.314
## .A1 ~~
## .A6 0.173 0.040 4.359 0.000 0.173 0.286
## Warmth ~~
## Dominance 0.283 0.061 4.629 0.000 0.283 0.283
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A1 0.755 0.065 11.539 0.000 0.755 0.659
## .A2 0.625 0.056 11.172 0.000 0.625 0.586
## .A3 0.732 0.065 11.232 0.000 0.732 0.595
## .A4 0.620 0.055 11.229 0.000 0.620 0.623
## .A5 0.488 0.045 10.739 0.000 0.488 0.528
## .A6 0.488 0.043 11.413 0.000 0.488 0.635
## .A7 0.635 0.055 11.562 0.000 0.635 0.649
## .A8 0.744 0.063 11.782 0.000 0.744 0.692
## .A9 0.558 0.055 10.179 0.000 0.558 0.476
## .A10 0.916 0.074 12.440 0.000 0.916 0.862
## .D1 0.399 0.043 9.195 0.000 0.399 0.403
## .D2 0.744 0.065 11.458 0.000 0.744 0.641
## .D3 0.939 0.075 12.468 0.000 0.939 0.876
## .D4 0.823 0.068 12.163 0.000 0.823 0.788
## .D5 0.502 0.047 10.643 0.000 0.502 0.529
## .D6 0.603 0.051 11.903 0.000 0.603 0.727
## .D7 0.652 0.061 10.737 0.000 0.652 0.548
## .D8 0.572 0.047 12.294 0.000 0.572 0.824
## .D9 0.652 0.056 11.573 0.000 0.652 0.685
## .D10 0.858 0.072 11.907 0.000 0.858 0.728
## Warmth 1.000 1.000 1.000
## Dominance 1.000 1.000 1.000
##
## R-Square:
## Estimate
## A1 0.341
## A2 0.414
## A3 0.405
## A4 0.377
## A5 0.472
## A6 0.365
## A7 0.351
## A8 0.308
## A9 0.524
## A10 0.138
## D1 0.597
## D2 0.359
## D3 0.124
## D4 0.212
## D5 0.471
## D6 0.273
## D7 0.452
## D8 0.176
## D9 0.315
## D10 0.272#
cfa_fit_mod <- cfa(cfa_syntax_mod, data = dat, std.lv = TRUE, missing = "ML")
head(modificationIndices(cfa_fit_mod, sort. = TRUE, power = TRUE))## lhs op rhs mi epc sepc.all delta ncp power decision
## 157 A5 ~~ A6 26.344 0.147 0.302 0.1 12.170 0.937 *epc:m*
## 110 A2 ~~ A6 21.020 0.145 0.265 0.1 9.990 0.885 *epc:m*
## 90 A1 ~~ A3 20.699 0.191 0.257 0.1 5.678 0.664 **(m)**
## 249 D3 ~~ D4 17.265 0.204 0.230 0.1 4.152 0.531 **(m)**
## 69 Warmth =~ D1 13.414 0.167 0.167 0.1 4.826 0.594 **(m)**
## 131 A3 ~~ A10 12.604 -0.170 -0.206 0.1 4.387 0.553 **(m)**#####
#Modification A5~~A6
cfa_syntax_mod <- " Warmth =~ A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + A9 + A10
Dominance =~ D1 + D2 + D3 + D4 + D5 + D6 + D7 + D8 + D9 + D10
A4~~A9
D7~~D9
A1~~A6
A5~~A6
"
cfa_fit_mod <- cfa(cfa_syntax_mod, data = dat, std.lv = TRUE)
summary(cfa_fit_mod,standardize= TRUE, rsquare= TRUE)## lavaan 0.6.15 ended normally after 24 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 45
##
## Used Total
## Number of observations 328 358
##
## Model Test User Model:
##
## Test statistic 346.172
## Degrees of freedom 165
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Warmth =~
## A1 0.620 0.058 10.594 0.000 0.620 0.579
## A2 0.644 0.055 11.610 0.000 0.644 0.623
## A3 0.724 0.059 12.305 0.000 0.724 0.653
## A4 0.631 0.054 11.641 0.000 0.631 0.632
## A5 0.626 0.051 12.249 0.000 0.626 0.651
## A6 0.482 0.048 9.956 0.000 0.482 0.554
## A7 0.589 0.054 10.983 0.000 0.589 0.596
## A8 -0.592 0.057 -10.417 0.000 -0.592 -0.570
## A9 -0.806 0.055 -14.554 0.000 -0.806 -0.744
## A10 -0.400 0.059 -6.721 0.000 -0.400 -0.388
## Dominance =~
## D1 0.770 0.050 15.378 0.000 0.770 0.773
## D2 0.645 0.058 11.044 0.000 0.645 0.599
## D3 0.365 0.060 6.059 0.000 0.365 0.352
## D4 0.470 0.058 8.120 0.000 0.470 0.460
## D5 0.669 0.051 13.116 0.000 0.669 0.686
## D6 0.476 0.051 9.385 0.000 0.476 0.522
## D7 -0.733 0.058 -12.730 0.000 -0.733 -0.672
## D8 -0.350 0.048 -7.342 0.000 -0.350 -0.420
## D9 -0.548 0.054 -10.132 0.000 -0.548 -0.562
## D10 -0.567 0.060 -9.377 0.000 -0.567 -0.522
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A4 ~~
## .A9 -0.199 0.043 -4.683 0.000 -0.199 -0.356
## .D7 ~~
## .D9 0.205 0.045 4.593 0.000 0.205 0.314
## .A1 ~~
## .A6 0.182 0.038 4.785 0.000 0.182 0.288
## .A5 ~~
## .A6 0.157 0.033 4.739 0.000 0.157 0.297
## Warmth ~~
## Dominance 0.282 0.061 4.603 0.000 0.282 0.282
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A1 0.762 0.066 11.585 0.000 0.762 0.665
## .A2 0.652 0.058 11.277 0.000 0.652 0.612
## .A3 0.707 0.064 11.016 0.000 0.707 0.574
## .A4 0.597 0.055 10.937 0.000 0.597 0.600
## .A5 0.533 0.048 11.016 0.000 0.533 0.576
## .A6 0.524 0.045 11.770 0.000 0.524 0.693
## .A7 0.631 0.055 11.484 0.000 0.631 0.645
## .A8 0.726 0.062 11.649 0.000 0.726 0.675
## .A9 0.524 0.054 9.692 0.000 0.524 0.446
## .A10 0.903 0.073 12.385 0.000 0.903 0.850
## .D1 0.399 0.043 9.195 0.000 0.399 0.403
## .D2 0.744 0.065 11.459 0.000 0.744 0.642
## .D3 0.939 0.075 12.468 0.000 0.939 0.876
## .D4 0.823 0.068 12.162 0.000 0.823 0.788
## .D5 0.502 0.047 10.644 0.000 0.502 0.529
## .D6 0.603 0.051 11.905 0.000 0.603 0.727
## .D7 0.652 0.061 10.738 0.000 0.652 0.548
## .D8 0.572 0.047 12.292 0.000 0.572 0.823
## .D9 0.651 0.056 11.570 0.000 0.651 0.684
## .D10 0.858 0.072 11.907 0.000 0.858 0.728
## Warmth 1.000 1.000 1.000
## Dominance 1.000 1.000 1.000
##
## R-Square:
## Estimate
## A1 0.335
## A2 0.388
## A3 0.426
## A4 0.400
## A5 0.424
## A6 0.307
## A7 0.355
## A8 0.325
## A9 0.554
## A10 0.150
## D1 0.597
## D2 0.358
## D3 0.124
## D4 0.212
## D5 0.471
## D6 0.273
## D7 0.452
## D8 0.177
## D9 0.316
## D10 0.272#
cfa_fit_mod <- cfa(cfa_syntax_mod, data = dat, std.lv = TRUE, missing = "ML")
head(modificationIndices(cfa_fit_mod, sort. = TRUE, power = TRUE))## lhs op rhs mi epc sepc.all delta ncp power decision
## 111 A2 ~~ A6 22.828 0.148 0.256 0.1 10.440 0.898 *epc:m*
## 91 A1 ~~ A3 18.024 0.179 0.244 0.1 5.621 0.659 **(m)**
## 249 D3 ~~ D4 17.272 0.204 0.230 0.1 4.152 0.531 **(m)**
## 70 Warmth =~ D1 13.758 0.169 0.170 0.1 4.812 0.592 **(m)**
## 94 A1 ~~ A7 11.769 -0.131 -0.194 0.1 6.872 0.746 **(m)**
## 79 Warmth =~ D10 11.380 0.195 0.179 0.1 2.996 0.409 **(m)**#####
#Modification A2~~A6
cfa_syntax_mod <- " Warmth =~ A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + A9 + A10
Dominance =~ D1 + D2 + D3 + D4 + D5 + D6 + D7 + D8 + D9 + D10
A4~~A9
D7~~D9
A1~~A6
A5~~A6
A2~~A6
"
cfa_fit_mod <- cfa(cfa_syntax_mod, data = dat, std.lv = TRUE)
summary(cfa_fit_mod,standardize= TRUE, rsquare= TRUE)## lavaan 0.6.15 ended normally after 24 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 46
##
## Used Total
## Number of observations 328 358
##
## Model Test User Model:
##
## Test statistic 326.103
## Degrees of freedom 164
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Warmth =~
## A1 0.619 0.058 10.594 0.000 0.619 0.579
## A2 0.633 0.056 11.356 0.000 0.633 0.613
## A3 0.731 0.059 12.447 0.000 0.731 0.659
## A4 0.631 0.054 11.628 0.000 0.631 0.632
## A5 0.624 0.051 12.213 0.000 0.624 0.649
## A6 0.455 0.049 9.328 0.000 0.455 0.528
## A7 0.588 0.054 10.937 0.000 0.588 0.594
## A8 -0.592 0.057 -10.410 0.000 -0.592 -0.570
## A9 -0.810 0.055 -14.643 0.000 -0.810 -0.748
## A10 -0.404 0.059 -6.793 0.000 -0.404 -0.392
## Dominance =~
## D1 0.770 0.050 15.379 0.000 0.770 0.773
## D2 0.645 0.058 11.044 0.000 0.645 0.599
## D3 0.365 0.060 6.058 0.000 0.365 0.352
## D4 0.470 0.058 8.121 0.000 0.470 0.460
## D5 0.669 0.051 13.115 0.000 0.669 0.686
## D6 0.475 0.051 9.381 0.000 0.475 0.522
## D7 -0.733 0.058 -12.725 0.000 -0.733 -0.672
## D8 -0.351 0.048 -7.348 0.000 -0.351 -0.421
## D9 -0.548 0.054 -10.139 0.000 -0.548 -0.562
## D10 -0.567 0.060 -9.379 0.000 -0.567 -0.522
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A4 ~~
## .A9 -0.196 0.043 -4.618 0.000 -0.196 -0.354
## .D7 ~~
## .D9 0.204 0.045 4.591 0.000 0.204 0.314
## .A1 ~~
## .A6 0.194 0.037 5.243 0.000 0.194 0.304
## .A5 ~~
## .A6 0.152 0.032 4.801 0.000 0.152 0.283
## .A2 ~~
## .A6 0.141 0.034 4.188 0.000 0.141 0.236
## Warmth ~~
## Dominance 0.285 0.061 4.647 0.000 0.285 0.285
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A1 0.762 0.066 11.588 0.000 0.762 0.665
## .A2 0.666 0.059 11.351 0.000 0.666 0.625
## .A3 0.697 0.064 10.939 0.000 0.697 0.566
## .A4 0.597 0.055 10.908 0.000 0.597 0.600
## .A5 0.535 0.048 11.035 0.000 0.535 0.578
## .A6 0.535 0.045 12.000 0.000 0.535 0.721
## .A7 0.633 0.055 11.486 0.000 0.633 0.647
## .A8 0.726 0.062 11.641 0.000 0.726 0.675
## .A9 0.517 0.054 9.597 0.000 0.517 0.441
## .A10 0.900 0.073 12.371 0.000 0.900 0.847
## .D1 0.399 0.043 9.195 0.000 0.399 0.402
## .D2 0.744 0.065 11.459 0.000 0.744 0.642
## .D3 0.939 0.075 12.468 0.000 0.939 0.876
## .D4 0.823 0.068 12.162 0.000 0.823 0.788
## .D5 0.502 0.047 10.645 0.000 0.502 0.529
## .D6 0.603 0.051 11.906 0.000 0.603 0.727
## .D7 0.653 0.061 10.740 0.000 0.653 0.548
## .D8 0.572 0.047 12.292 0.000 0.572 0.823
## .D9 0.651 0.056 11.568 0.000 0.651 0.684
## .D10 0.858 0.072 11.907 0.000 0.858 0.727
## Warmth 1.000 1.000 1.000
## Dominance 1.000 1.000 1.000
##
## R-Square:
## Estimate
## A1 0.335
## A2 0.375
## A3 0.434
## A4 0.400
## A5 0.422
## A6 0.279
## A7 0.353
## A8 0.325
## A9 0.559
## A10 0.153
## D1 0.598
## D2 0.358
## D3 0.124
## D4 0.212
## D5 0.471
## D6 0.273
## D7 0.452
## D8 0.177
## D9 0.316
## D10 0.273#
cfa_fit_mod <- cfa(cfa_syntax_mod, data = dat, std.lv = TRUE, missing = "ML")
head(modificationIndices(cfa_fit_mod, sort. = TRUE, power = TRUE))## lhs op rhs mi epc sepc.all delta ncp power decision
## 249 D3 ~~ D4 17.275 0.204 0.230 0.1 4.152 0.531 **(m)**
## 92 A1 ~~ A3 14.978 0.164 0.224 0.1 5.600 0.658 **(m)**
## 71 Warmth =~ D1 13.696 0.169 0.169 0.1 4.803 0.592 **(m)**
## 111 A2 ~~ A5 13.344 0.136 0.229 0.1 7.181 0.764 *epc:m*
## 95 A1 ~~ A7 13.085 -0.139 -0.205 0.1 6.793 0.741 **(m)**
## 83 Dominance =~ A3 11.604 -0.190 -0.169 0.1 3.214 0.434 **(m)**#####
#Modification D3~~D4
cfa_syntax_mod <- " Warmth =~ A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + A9 + A10
Dominance =~ D1 + D2 + D3 + D4 + D5 + D6 + D7 + D8 + D9 + D10
A4~~A9
D7~~D9
A1~~A6
A5~~A6
A2~~A6
D3~~D4
"
cfa_fit_mod <- cfa(cfa_syntax_mod, data = dat, std.lv = TRUE)
summary(cfa_fit_mod,standardize= TRUE, rsquare= TRUE)## lavaan 0.6.15 ended normally after 23 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 47
##
## Used Total
## Number of observations 328 358
##
## Model Test User Model:
##
## Test statistic 311.685
## Degrees of freedom 163
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Warmth =~
## A1 0.620 0.058 10.597 0.000 0.620 0.579
## A2 0.633 0.056 11.355 0.000 0.633 0.612
## A3 0.731 0.059 12.448 0.000 0.731 0.659
## A4 0.631 0.054 11.627 0.000 0.631 0.632
## A5 0.624 0.051 12.214 0.000 0.624 0.649
## A6 0.455 0.049 9.329 0.000 0.455 0.528
## A7 0.588 0.054 10.938 0.000 0.588 0.594
## A8 -0.591 0.057 -10.410 0.000 -0.591 -0.570
## A9 -0.810 0.055 -14.642 0.000 -0.810 -0.748
## A10 -0.404 0.059 -6.793 0.000 -0.404 -0.392
## Dominance =~
## D1 0.776 0.050 15.521 0.000 0.776 0.779
## D2 0.647 0.058 11.082 0.000 0.647 0.601
## D3 0.343 0.061 5.652 0.000 0.343 0.331
## D4 0.454 0.058 7.802 0.000 0.454 0.445
## D5 0.672 0.051 13.187 0.000 0.672 0.689
## D6 0.473 0.051 9.326 0.000 0.473 0.520
## D7 -0.732 0.058 -12.687 0.000 -0.732 -0.671
## D8 -0.349 0.048 -7.307 0.000 -0.349 -0.419
## D9 -0.548 0.054 -10.129 0.000 -0.548 -0.562
## D10 -0.564 0.061 -9.322 0.000 -0.564 -0.520
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A4 ~~
## .A9 -0.197 0.043 -4.620 0.000 -0.197 -0.354
## .D7 ~~
## .D9 0.205 0.045 4.595 0.000 0.205 0.314
## .A1 ~~
## .A6 0.194 0.037 5.242 0.000 0.194 0.304
## .A5 ~~
## .A6 0.152 0.032 4.801 0.000 0.152 0.283
## .A2 ~~
## .A6 0.141 0.034 4.188 0.000 0.141 0.236
## .D3 ~~
## .D4 0.192 0.053 3.640 0.000 0.192 0.214
## Warmth ~~
## Dominance 0.286 0.061 4.672 0.000 0.286 0.286
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A1 0.762 0.066 11.588 0.000 0.762 0.665
## .A2 0.666 0.059 11.351 0.000 0.666 0.625
## .A3 0.696 0.064 10.939 0.000 0.696 0.566
## .A4 0.597 0.055 10.909 0.000 0.597 0.600
## .A5 0.535 0.048 11.035 0.000 0.535 0.578
## .A6 0.535 0.045 12.000 0.000 0.535 0.721
## .A7 0.633 0.055 11.486 0.000 0.633 0.647
## .A8 0.726 0.062 11.641 0.000 0.726 0.675
## .A9 0.517 0.054 9.598 0.000 0.517 0.441
## .A10 0.900 0.073 12.371 0.000 0.900 0.847
## .D1 0.390 0.043 9.021 0.000 0.390 0.393
## .D2 0.741 0.065 11.433 0.000 0.741 0.639
## .D3 0.955 0.076 12.500 0.000 0.955 0.890
## .D4 0.838 0.069 12.204 0.000 0.838 0.802
## .D5 0.498 0.047 10.585 0.000 0.498 0.525
## .D6 0.605 0.051 11.911 0.000 0.605 0.730
## .D7 0.654 0.061 10.734 0.000 0.654 0.550
## .D8 0.573 0.047 12.294 0.000 0.573 0.825
## .D9 0.651 0.056 11.559 0.000 0.651 0.684
## .D10 0.861 0.072 11.912 0.000 0.861 0.730
## Warmth 1.000 1.000 1.000
## Dominance 1.000 1.000 1.000
##
## R-Square:
## Estimate
## A1 0.335
## A2 0.375
## A3 0.434
## A4 0.400
## A5 0.422
## A6 0.279
## A7 0.353
## A8 0.325
## A9 0.559
## A10 0.153
## D1 0.607
## D2 0.361
## D3 0.110
## D4 0.198
## D5 0.475
## D6 0.270
## D7 0.450
## D8 0.175
## D9 0.316
## D10 0.270#
cfa_fit_mod <- cfa(cfa_syntax_mod, data = dat, std.lv = TRUE, missing = "ML")
head(modificationIndices(cfa_fit_mod, sort. = TRUE, power = TRUE))## lhs op rhs mi epc sepc.all delta ncp power decision
## 93 A1 ~~ A3 14.959 0.163 0.224 0.1 5.601 0.658 **(m)**
## 72 Warmth =~ D1 13.629 0.168 0.169 0.1 4.821 0.593 **(m)**
## 112 A2 ~~ A5 13.350 0.136 0.229 0.1 7.181 0.764 *epc:m*
## 96 A1 ~~ A7 13.102 -0.139 -0.205 0.1 6.794 0.741 **(m)**
## 84 Dominance =~ A3 11.463 -0.189 -0.168 0.1 3.208 0.433 **(m)**
## 147 A4 ~~ A8 11.178 -0.121 -0.183 0.1 7.653 0.790 *epc:m*#####
##
#####
#Modification A1~~A3
cfa_syntax_mod <- " Warmth =~ A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + A9 + A10
Dominance =~ D1 + D2 + D3 + D4 + D5 + D6 + D7 + D8 + D9 + D10
A4~~A9
D7~~D9
A1~~A6
A5~~A6
A2~~A6
D3~~D4
A1~~A3
"
cfa_fit_mod <- cfa(cfa_syntax_mod, data = dat, std.lv = TRUE)
summary(cfa_fit_mod,standardize= TRUE, rsquare= TRUE)## lavaan 0.6.15 ended normally after 24 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 48
##
## Used Total
## Number of observations 328 358
##
## Model Test User Model:
##
## Test statistic 297.510
## Degrees of freedom 162
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Warmth =~
## A1 0.580 0.060 9.686 0.000 0.580 0.542
## A2 0.635 0.056 11.356 0.000 0.635 0.615
## A3 0.700 0.060 11.682 0.000 0.700 0.631
## A4 0.643 0.054 11.823 0.000 0.643 0.645
## A5 0.619 0.051 12.039 0.000 0.619 0.644
## A6 0.457 0.049 9.413 0.000 0.457 0.533
## A7 0.601 0.054 11.203 0.000 0.601 0.608
## A8 -0.603 0.057 -10.603 0.000 -0.603 -0.581
## A9 -0.820 0.055 -14.781 0.000 -0.820 -0.757
## A10 -0.400 0.060 -6.709 0.000 -0.400 -0.388
## Dominance =~
## D1 0.775 0.050 15.512 0.000 0.775 0.779
## D2 0.647 0.058 11.078 0.000 0.647 0.601
## D3 0.343 0.061 5.654 0.000 0.343 0.331
## D4 0.455 0.058 7.806 0.000 0.455 0.445
## D5 0.672 0.051 13.187 0.000 0.672 0.690
## D6 0.473 0.051 9.322 0.000 0.473 0.520
## D7 -0.732 0.058 -12.693 0.000 -0.732 -0.671
## D8 -0.349 0.048 -7.312 0.000 -0.349 -0.419
## D9 -0.548 0.054 -10.130 0.000 -0.548 -0.562
## D10 -0.564 0.061 -9.323 0.000 -0.564 -0.520
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A4 ~~
## .A9 -0.180 0.043 -4.211 0.000 -0.180 -0.334
## .D7 ~~
## .D9 0.205 0.045 4.591 0.000 0.205 0.314
## .A1 ~~
## .A6 0.200 0.036 5.543 0.000 0.200 0.307
## .A5 ~~
## .A6 0.146 0.032 4.601 0.000 0.146 0.274
## .A2 ~~
## .A6 0.130 0.034 3.891 0.000 0.130 0.221
## .D3 ~~
## .D4 0.192 0.053 3.638 0.000 0.192 0.214
## .A1 ~~
## .A3 0.170 0.048 3.560 0.000 0.170 0.219
## Warmth ~~
## Dominance 0.283 0.062 4.597 0.000 0.283 0.283
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .A1 0.809 0.069 11.773 0.000 0.809 0.706
## .A2 0.664 0.059 11.264 0.000 0.664 0.622
## .A3 0.742 0.067 11.066 0.000 0.742 0.602
## .A4 0.581 0.055 10.637 0.000 0.581 0.584
## .A5 0.541 0.049 11.000 0.000 0.541 0.585
## .A6 0.527 0.044 11.940 0.000 0.527 0.716
## .A7 0.617 0.054 11.322 0.000 0.617 0.631
## .A8 0.713 0.062 11.518 0.000 0.713 0.662
## .A9 0.500 0.054 9.218 0.000 0.500 0.427
## .A10 0.903 0.073 12.361 0.000 0.903 0.849
## .D1 0.391 0.043 9.025 0.000 0.391 0.394
## .D2 0.741 0.065 11.434 0.000 0.741 0.639
## .D3 0.955 0.076 12.499 0.000 0.955 0.890
## .D4 0.837 0.069 12.203 0.000 0.837 0.802
## .D5 0.498 0.047 10.583 0.000 0.498 0.525
## .D6 0.605 0.051 11.911 0.000 0.605 0.730
## .D7 0.654 0.061 10.729 0.000 0.654 0.550
## .D8 0.573 0.047 12.292 0.000 0.573 0.824
## .D9 0.651 0.056 11.557 0.000 0.651 0.684
## .D10 0.861 0.072 11.911 0.000 0.861 0.730
## Warmth 1.000 1.000 1.000
## Dominance 1.000 1.000 1.000
##
## R-Square:
## Estimate
## A1 0.294
## A2 0.378
## A3 0.398
## A4 0.416
## A5 0.415
## A6 0.284
## A7 0.369
## A8 0.338
## A9 0.573
## A10 0.151
## D1 0.606
## D2 0.361
## D3 0.110
## D4 0.198
## D5 0.475
## D6 0.270
## D7 0.450
## D8 0.176
## D9 0.316
## D10 0.270#
cfa_fit_mod <- cfa(cfa_syntax_mod, data = dat, std.lv = TRUE, missing = "ML")
head(modificationIndices(cfa_fit_mod, sort. = TRUE, power = TRUE))## lhs op rhs mi epc sepc.all delta ncp power decision
## 85 Dominance =~ A3 13.814 -0.203 -0.180 0.1 3.365 0.450 **(m)**
## 112 A2 ~~ A5 13.661 0.140 0.235 0.1 7.016 0.755 *epc:m*
## 73 Warmth =~ D1 13.339 0.167 0.167 0.1 4.792 0.591 **(m)**
## 133 A3 ~~ A10 11.917 -0.159 -0.193 0.1 4.730 0.585 **(m)**
## 83 Dominance =~ A1 11.492 0.172 0.160 0.1 3.889 0.505 **(m)**
## 82 Warmth =~ D10 11.136 0.194 0.178 0.1 2.961 0.406 **(m)**The fit of the model has improved.
library(corrplot)
corrplot(
resid(cfa_fit, type = "cor")$cov,
type = "lower", is.corr = FALSE )
##########
library(corrplot)
corrplot(
resid(cfa_fit_mod, type = "cor")$cov,
type = "lower", is.corr = FALSE)
Part 4: Model diagram for both original model, and final model.
#Part 4: Model diagram for both original model, and final model.
library(lavaanPlot)## Warning: package 'lavaanPlot' was built under R version 4.2.2lavaanPlot(model = cfa_fit, coefs = TRUE, covs = TRUE, stars = "regress")##### modified model
library(lavaanPlot)
lavaanPlot(model = cfa_fit_mod, coefs = TRUE, covs = TRUE, stars = "regress")