Conduct a Path Analysis, a Confirmatory Factor Analysis and a Structure Equation
#Conduct a Path Analysis ##Study the correlation between the variables Let’s study the correlation and the covariance between the variables First Group
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──## ✓ ggplot2 3.3.2 ✓ purrr 0.3.4
## ✓ tibble 3.0.4 ✓ dplyr 1.0.2
## ✓ tidyr 1.1.2 ✓ stringr 1.4.0
## ✓ readr 1.4.0 ✓ forcats 0.5.0## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()require(dplyr)
library(lavaan)## This is lavaan 0.6-7## lavaan is BETA software! Please report any bugs.library(psych)##
## Attaching package: 'psych'## The following object is masked from 'package:lavaan':
##
## cor2cov## The following objects are masked from 'package:ggplot2':
##
## %+%, alphalibrary(semPlot)## Registered S3 methods overwritten by 'huge':
## method from
## plot.sim BDgraph
## print.sim BDgraphdf <- read_csv("/home/asma/Desktop/CFA_FINAL/Factor_Analysis.csv")##
## ── Column specification ────────────────────────────────────────────────────────
## cols(
## .default = col_double()
## )
## ℹ Use `spec()` for the full column specifications.covariance_matrix <- round(cov(df[,1:5]),2)
# create a correlation matrix
correlation_matrix <- cor(df[,1:5])
covariance_matrix## sector_work_class Career_day Career_day_help Relation
## sector_work_class 0.13 0.01 -0.04 0.00
## Career_day 0.01 0.17 0.03 0.01
## Career_day_help -0.04 0.03 0.25 -0.11
## Relation 0.00 0.01 -0.11 0.21
## Cur_salar -0.05 0.05 0.32 -0.29
## Cur_salar
## sector_work_class -0.05
## Career_day 0.05
## Career_day_help 0.32
## Relation -0.29
## Cur_salar 1.22correlation_matrix## sector_work_class Career_day Career_day_help Relation
## sector_work_class 1.000000000 0.08848601 -0.2195342 0.005246782
## Career_day 0.088486013 1.00000000 0.1296595 0.029816606
## Career_day_help -0.219534237 0.12965953 1.0000000 -0.476172288
## Relation 0.005246782 0.02981661 -0.4761723 1.000000000
## Cur_salar -0.131292225 0.09868834 0.5852821 -0.581023873
## Cur_salar
## sector_work_class -0.13129223
## Career_day 0.09868834
## Career_day_help 0.58528208
## Relation -0.58102387
## Cur_salar 1.00000000Second group
# create a correlation matrix
library(semPlot)
df <- read_csv("/home/asma/Desktop/CFA_FINAL/Factor_Analysis.csv")##
## ── Column specification ────────────────────────────────────────────────────────
## cols(
## .default = col_double()
## )
## ℹ Use `spec()` for the full column specifications.covariance_matrix <- round(cov(df[,6:19]),2)
correlation_matrix <- cor(df[,6:19])
covariance_matrix## PA1 PA2 PA3 PA4 PA5 PA6 PA7 PA8 PA9 PA10 PA11 PA12 PA13 PA14
## PA1 0.92 0.50 0.51 0.42 0.53 0.51 0.60 0.49 0.51 0.47 0.54 0.54 0.52 0.46
## PA2 0.50 0.88 0.65 0.50 0.51 0.47 0.53 0.47 0.49 0.57 0.55 0.52 0.51 0.54
## PA3 0.51 0.65 0.89 0.55 0.45 0.44 0.52 0.46 0.43 0.57 0.58 0.51 0.47 0.42
## PA4 0.42 0.50 0.55 0.91 0.65 0.59 0.55 0.54 0.52 0.46 0.41 0.52 0.53 0.45
## PA5 0.53 0.51 0.45 0.65 1.14 0.65 0.68 0.55 0.68 0.55 0.52 0.73 0.65 0.66
## PA6 0.51 0.47 0.44 0.59 0.65 1.03 0.65 0.54 0.57 0.50 0.41 0.60 0.45 0.64
## PA7 0.60 0.53 0.52 0.55 0.68 0.65 0.99 0.55 0.52 0.52 0.49 0.63 0.54 0.53
## PA8 0.49 0.47 0.46 0.54 0.55 0.54 0.55 1.31 0.66 0.66 0.49 0.57 0.41 0.46
## PA9 0.51 0.49 0.43 0.52 0.68 0.57 0.52 0.66 1.03 0.64 0.52 0.64 0.48 0.54
## PA10 0.47 0.57 0.57 0.46 0.55 0.50 0.52 0.66 0.64 1.29 0.76 0.70 0.55 0.55
## PA11 0.54 0.55 0.58 0.41 0.52 0.41 0.49 0.49 0.52 0.76 1.11 0.75 0.68 0.64
## PA12 0.54 0.52 0.51 0.52 0.73 0.60 0.63 0.57 0.64 0.70 0.75 1.34 0.82 0.66
## PA13 0.52 0.51 0.47 0.53 0.65 0.45 0.54 0.41 0.48 0.55 0.68 0.82 1.24 0.61
## PA14 0.46 0.54 0.42 0.45 0.66 0.64 0.53 0.46 0.54 0.55 0.64 0.66 0.61 2.03correlation_matrix## PA1 PA2 PA3 PA4 PA5 PA6 PA7
## PA1 1.0000000 0.5546416 0.5696548 0.4593138 0.5186495 0.5230535 0.6289039
## PA2 0.5546416 1.0000000 0.7380481 0.5533564 0.5134730 0.4968103 0.5662640
## PA3 0.5696548 0.7380481 1.0000000 0.6148604 0.4459097 0.4575497 0.5529272
## PA4 0.4593138 0.5533564 0.6148604 1.0000000 0.6400842 0.6135089 0.5814082
## PA5 0.5186495 0.5134730 0.4459097 0.6400842 1.0000000 0.5983047 0.6423391
## PA6 0.5230535 0.4968103 0.4575497 0.6135089 0.5983047 1.0000000 0.6401350
## PA7 0.6289039 0.5662640 0.5529272 0.5814082 0.6423391 0.6401350 1.0000000
## PA8 0.4495319 0.4329473 0.4284650 0.4931994 0.4523979 0.4600253 0.4792444
## PA9 0.5303571 0.5118894 0.4469960 0.5402925 0.6324713 0.5510269 0.5188057
## PA10 0.4356556 0.5332379 0.5363535 0.4230978 0.4505303 0.4345094 0.4638834
## PA11 0.5370137 0.5597673 0.5850084 0.4135218 0.4610475 0.3831567 0.4675466
## PA12 0.4917534 0.4738689 0.4708482 0.4750648 0.5913379 0.5132133 0.5472307
## PA13 0.4900643 0.4893092 0.4521673 0.4978824 0.5465732 0.4015520 0.4904514
## PA14 0.3356502 0.4043172 0.3099145 0.3320833 0.4325805 0.4401709 0.3707710
## PA8 PA9 PA10 PA11 PA12 PA13 PA14
## PA1 0.4495319 0.5303571 0.4356556 0.5370137 0.4917534 0.4900643 0.3356502
## PA2 0.4329473 0.5118894 0.5332379 0.5597673 0.4738689 0.4893092 0.4043172
## PA3 0.4284650 0.4469960 0.5363535 0.5850084 0.4708482 0.4521673 0.3099145
## PA4 0.4931994 0.5402925 0.4230978 0.4135218 0.4750648 0.4978824 0.3320833
## PA5 0.4523979 0.6324713 0.4505303 0.4610475 0.5913379 0.5465732 0.4325805
## PA6 0.4600253 0.5510269 0.4345094 0.3831567 0.5132133 0.4015520 0.4401709
## PA7 0.4792444 0.5188057 0.4638834 0.4675466 0.5472307 0.4904514 0.3707710
## PA8 1.0000000 0.5685952 0.5094052 0.4086080 0.4323614 0.3243631 0.2788873
## PA9 0.5685952 1.0000000 0.5603399 0.4855153 0.5441025 0.4217423 0.3740137
## PA10 0.5094052 0.5603399 1.0000000 0.6367229 0.5299883 0.4325425 0.3389642
## PA11 0.4086080 0.4855153 0.6367229 1.0000000 0.6162374 0.5808169 0.4238692
## PA12 0.4323614 0.5441025 0.5299883 0.6162374 1.0000000 0.6356367 0.3971059
## PA13 0.3243631 0.4217423 0.4325425 0.5808169 0.6356367 1.0000000 0.3835737
## PA14 0.2788873 0.3740137 0.3389642 0.4238692 0.3971059 0.3835737 1.0000000Third group
# create a correlation matrix
library(semPlot)
df <- read_csv("/home/asma/Desktop/CFA_FINAL/Factor_Analysis.csv")##
## ── Column specification ────────────────────────────────────────────────────────
## cols(
## .default = col_double()
## )
## ℹ Use `spec()` for the full column specifications.covariance_matrix <- round(cov(df[,20:31]),2)
correlation_matrix <- cor(df[,20:31])
covariance_matrix## SA1 SA2 SA3 SA4 SA5 SA6 SA7 SA8 SA9 SA10 SA11 SA12
## SA1 0.96 0.65 0.67 0.47 0.57 0.50 0.51 0.51 0.45 0.41 0.47 0.59
## SA2 0.65 0.95 0.72 0.56 0.60 0.58 0.55 0.56 0.47 0.41 0.46 0.55
## SA3 0.67 0.72 1.00 0.61 0.58 0.58 0.59 0.58 0.56 0.45 0.49 0.55
## SA4 0.47 0.56 0.61 0.88 0.51 0.49 0.50 0.52 0.48 0.42 0.46 0.48
## SA5 0.57 0.60 0.58 0.51 0.93 0.46 0.45 0.44 0.48 0.43 0.49 0.56
## SA6 0.50 0.58 0.58 0.49 0.46 0.87 0.55 0.47 0.44 0.42 0.39 0.46
## SA7 0.51 0.55 0.59 0.50 0.45 0.55 0.82 0.45 0.45 0.50 0.43 0.46
## SA8 0.51 0.56 0.58 0.52 0.44 0.47 0.45 1.07 0.66 0.51 0.44 0.59
## SA9 0.45 0.47 0.56 0.48 0.48 0.44 0.45 0.66 0.95 0.53 0.47 0.49
## SA10 0.41 0.41 0.45 0.42 0.43 0.42 0.50 0.51 0.53 0.93 0.47 0.57
## SA11 0.47 0.46 0.49 0.46 0.49 0.39 0.43 0.44 0.47 0.47 0.99 0.57
## SA12 0.59 0.55 0.55 0.48 0.56 0.46 0.46 0.59 0.49 0.57 0.57 1.11correlation_matrix## SA1 SA2 SA3 SA4 SA5 SA6 SA7
## SA1 1.0000000 0.6835017 0.6873520 0.5107108 0.6013675 0.5479905 0.5760284
## SA2 0.6835017 1.0000000 0.7386661 0.6176969 0.6393782 0.6363041 0.6203962
## SA3 0.6873520 0.7386661 1.0000000 0.6473061 0.6035389 0.6243592 0.6464176
## SA4 0.5107108 0.6176969 0.6473061 1.0000000 0.5674268 0.5628966 0.5823837
## SA5 0.6013675 0.6393782 0.6035389 0.5674268 1.0000000 0.5163699 0.5121593
## SA6 0.5479905 0.6363041 0.6243592 0.5628966 0.5163699 1.0000000 0.6504141
## SA7 0.5760284 0.6203962 0.6464176 0.5823837 0.5121593 0.6504141 1.0000000
## SA8 0.4984632 0.5514133 0.5567643 0.5335931 0.4455758 0.4893906 0.4731259
## SA9 0.4754886 0.4969138 0.5770613 0.5274532 0.5140571 0.4807801 0.5080965
## SA10 0.4361209 0.4401855 0.4650327 0.4681250 0.4605738 0.4710334 0.5744776
## SA11 0.4798553 0.4779644 0.4903456 0.4946522 0.5078935 0.4243516 0.4792917
## SA12 0.5776685 0.5398073 0.5239512 0.4811109 0.5566634 0.4697337 0.4769087
## SA8 SA9 SA10 SA11 SA12
## SA1 0.4984632 0.4754886 0.4361209 0.4798553 0.5776685
## SA2 0.5514133 0.4969138 0.4401855 0.4779644 0.5398073
## SA3 0.5567643 0.5770613 0.4650327 0.4903456 0.5239512
## SA4 0.5335931 0.5274532 0.4681250 0.4946522 0.4811109
## SA5 0.4455758 0.5140571 0.4605738 0.5078935 0.5566634
## SA6 0.4893906 0.4807801 0.4710334 0.4243516 0.4697337
## SA7 0.4731259 0.5080965 0.5744776 0.4792917 0.4769087
## SA8 1.0000000 0.6503222 0.5111268 0.4236922 0.5370809
## SA9 0.6503222 1.0000000 0.5653181 0.4873760 0.4764728
## SA10 0.5111268 0.5653181 1.0000000 0.4930643 0.5638951
## SA11 0.4236922 0.4873760 0.4930643 1.0000000 0.5453459
## SA12 0.5370809 0.4764728 0.5638951 0.5453459 1.0000000Fourth group
# create a correlation matrix
library(semPlot)
df <- read_csv("/home/asma/Desktop/CFA_FINAL/Factor_Analysis.csv")##
## ── Column specification ────────────────────────────────────────────────────────
## cols(
## .default = col_double()
## )
## ℹ Use `spec()` for the full column specifications.covariance_matrix <- round(cov(df[,32:44]),2)
correlation_matrix <- cor(df[,32:49])
covariance_matrix## SA13 IS1 IS2 IS3 IS4 IS5 IS6 IS7 IS8 IS9 IS10 IS11 IS12
## SA13 1.01 0.37 0.42 0.43 0.45 0.34 0.41 0.32 0.43 0.29 0.36 0.37 0.35
## IS1 0.37 1.36 0.43 0.44 0.40 0.44 0.36 0.42 0.54 0.26 0.46 0.46 0.48
## IS2 0.42 0.43 1.03 0.66 0.60 0.41 0.36 0.44 0.59 0.33 0.46 0.34 0.52
## IS3 0.43 0.44 0.66 1.26 0.71 0.44 0.45 0.50 0.67 0.27 0.37 0.37 0.71
## IS4 0.45 0.40 0.60 0.71 1.24 0.47 0.46 0.43 0.52 0.25 0.35 0.47 0.52
## IS5 0.34 0.44 0.41 0.44 0.47 0.88 0.60 0.43 0.49 0.23 0.29 0.40 0.20
## IS6 0.41 0.36 0.36 0.45 0.46 0.60 1.00 0.35 0.28 0.22 0.24 0.38 0.10
## IS7 0.32 0.42 0.44 0.50 0.43 0.43 0.35 0.95 0.66 0.34 0.32 0.39 0.50
## IS8 0.43 0.54 0.59 0.67 0.52 0.49 0.28 0.66 1.69 0.41 0.40 0.57 0.74
## IS9 0.29 0.26 0.33 0.27 0.25 0.23 0.22 0.34 0.41 0.73 0.33 0.26 0.17
## IS10 0.36 0.46 0.46 0.37 0.35 0.29 0.24 0.32 0.40 0.33 1.17 0.41 0.51
## IS11 0.37 0.46 0.34 0.37 0.47 0.40 0.38 0.39 0.57 0.26 0.41 1.08 0.50
## IS12 0.35 0.48 0.52 0.71 0.52 0.20 0.10 0.50 0.74 0.17 0.51 0.50 1.98correlation_matrix## SA13 IS1 IS2 IS3 IS4 IS5 IS6
## SA13 1.0000000 0.3161633 0.4093483 0.3782502 0.4003895 0.3573227 0.4055616
## IS1 0.3161633 1.0000000 0.3623674 0.3361182 0.3064731 0.4036982 0.3081366
## IS2 0.4093483 0.3623674 1.0000000 0.5792443 0.5297738 0.4315697 0.3516593
## IS3 0.3782502 0.3361182 0.5792443 1.0000000 0.5639915 0.4166951 0.3962074
## IS4 0.4003895 0.3064731 0.5297738 0.5639915 1.0000000 0.4522712 0.4171133
## IS5 0.3573227 0.4036982 0.4315697 0.4166951 0.4522712 1.0000000 0.6375403
## IS6 0.4055616 0.3081366 0.3516593 0.3962074 0.4171133 0.6375403 1.0000000
## IS7 0.3294458 0.3691262 0.4451550 0.4601100 0.4005754 0.4689266 0.3587670
## IS8 0.3313304 0.3534015 0.4461337 0.4580708 0.3599498 0.4052301 0.2127666
## IS9 0.3380121 0.2654892 0.3740648 0.2779059 0.2635084 0.2823019 0.2592501
## IS10 0.3355500 0.3659229 0.4203843 0.3069887 0.2880858 0.2901289 0.2225302
## IS11 0.3583400 0.3849260 0.3266479 0.3168956 0.4055986 0.4108271 0.3620067
## IS12 0.2505388 0.2946100 0.3661291 0.4477396 0.3296530 0.1488925 0.0732025
## IS13 0.2615293 0.1582299 0.3005309 0.3069556 0.3545890 0.1443478 0.1800517
## IS14 0.2128691 0.0208829 0.1239028 0.1659061 0.3609494 0.2504481 0.3073466
## GA1 0.4672505 0.3631154 0.2879418 0.2466235 0.2752063 0.4597662 0.3401380
## GA2 0.3781681 0.3704435 0.2499464 0.1677393 0.2155627 0.3167812 0.2338764
## GA3 0.5627687 0.3049953 0.3155425 0.2676854 0.3534142 0.4533552 0.3925197
## IS7 IS8 IS9 IS10 IS11 IS12 IS13
## SA13 0.3294458 0.331330443 0.3380121 0.3355500 0.3583400 0.25053884 0.26152930
## IS1 0.3691262 0.353401533 0.2654892 0.3659229 0.3849260 0.29461001 0.15822994
## IS2 0.4451550 0.446133685 0.3740648 0.4203843 0.3266479 0.36612910 0.30053086
## IS3 0.4601100 0.458070836 0.2779059 0.3069887 0.3168956 0.44773957 0.30695557
## IS4 0.4005754 0.359949843 0.2635084 0.2880858 0.4055986 0.32965297 0.35458897
## IS5 0.4689266 0.405230053 0.2823019 0.2901289 0.4108271 0.14889253 0.14434777
## IS6 0.3587670 0.212766596 0.2592501 0.2225302 0.3620067 0.07320250 0.18005167
## IS7 1.0000000 0.521321342 0.4040559 0.3003033 0.3832554 0.36554958 0.22682720
## IS8 0.5213213 1.000000000 0.3649696 0.2857208 0.4219079 0.40265417 0.08357512
## IS9 0.4040559 0.364969594 1.0000000 0.3578973 0.2928365 0.14275882 0.25090169
## IS10 0.3003033 0.285720823 0.3578973 1.0000000 0.3669000 0.33638423 0.28340671
## IS11 0.3832554 0.421907946 0.2928365 0.3669000 1.0000000 0.34055335 0.23066094
## IS12 0.3655496 0.402654168 0.1427588 0.3363842 0.3405533 1.00000000 0.27228382
## IS13 0.2268272 0.083575120 0.2509017 0.2834067 0.2306609 0.27228382 1.00000000
## IS14 0.1397898 0.001296027 0.2387858 0.1991182 0.2279366 0.03877721 0.42357264
## GA1 0.3285342 0.330646456 0.2514986 0.2532271 0.2916454 0.08932213 0.07633492
## GA2 0.2931203 0.269842221 0.2133124 0.2059785 0.2698236 0.17645309 0.18592302
## GA3 0.3259466 0.320785674 0.2799685 0.2530560 0.2943454 0.13111886 0.18300860
## IS14 GA1 GA2 GA3
## SA13 0.212869079 0.46725045 0.3781681 0.5627687
## IS1 0.020882901 0.36311536 0.3704435 0.3049953
## IS2 0.123902751 0.28794177 0.2499464 0.3155425
## IS3 0.165906124 0.24662352 0.1677393 0.2676854
## IS4 0.360949427 0.27520629 0.2155627 0.3534142
## IS5 0.250448129 0.45976624 0.3167812 0.4533552
## IS6 0.307346575 0.34013796 0.2338764 0.3925197
## IS7 0.139789786 0.32853417 0.2931203 0.3259466
## IS8 0.001296027 0.33064646 0.2698422 0.3207857
## IS9 0.238785774 0.25149865 0.2133124 0.2799685
## IS10 0.199118185 0.25322706 0.2059785 0.2530560
## IS11 0.227936561 0.29164542 0.2698236 0.2943454
## IS12 0.038777213 0.08932213 0.1764531 0.1311189
## IS13 0.423572638 0.07633492 0.1859230 0.1830086
## IS14 1.000000000 0.13589024 0.1056496 0.1769258
## GA1 0.135890237 1.00000000 0.6836135 0.7093512
## GA2 0.105649632 0.68361353 1.0000000 0.5897725
## GA3 0.176925755 0.70935124 0.5897725 1.0000000Path Analysis:
model <-'PA3~ PA2+PA4+PA10+PA11
SA1~ SA2+SA3+SA4+SA5
GA3~GA1
IS8~IS7
IS2~ IS3+IS4
Cur_salar~ Relation+Career_day_help'
fit <- cfa(model, data=df, std.lv=TRUE)
summary(fit)## lavaan 0.6-7 ended normally after 37 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 35
##
## Number of observations 336
##
## Model Test User Model:
##
## Test statistic 256.852
## Degrees of freedom 70
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## PA3 ~
## PA2 0.461 0.045 10.329 0.000
## PA4 0.251 0.040 6.358 0.000
## PA10 0.056 0.037 1.525 0.127
## PA11 0.160 0.040 3.972 0.000
## SA1 ~
## SA2 0.284 0.057 4.949 0.000
## SA3 0.316 0.056 5.670 0.000
## SA4 -0.040 0.051 -0.779 0.436
## SA5 0.195 0.049 3.950 0.000
## GA3 ~
## GA1 0.687 0.039 17.572 0.000
## IS8 ~
## IS7 0.658 0.061 10.730 0.000
## IS2 ~
## IS3 0.350 0.046 7.611 0.000
## IS4 0.253 0.046 5.463 0.000
## Cur_salar ~
## Relation -0.947 0.109 -8.709 0.000
## Career_day_hlp 0.898 0.099 9.049 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .PA3 ~~
## .SA1 -0.005 0.020 -0.241 0.810
## .GA3 0.019 0.021 0.914 0.361
## .IS8 0.028 0.034 0.820 0.412
## .IS2 0.010 0.024 0.391 0.696
## .Cur_salar 0.029 0.025 1.147 0.252
## .SA1 ~~
## .GA3 0.096 0.025 3.928 0.000
## .IS8 0.045 0.039 1.134 0.257
## .IS2 0.025 0.028 0.904 0.366
## .Cur_salar 0.037 0.029 1.291 0.197
## .GA3 ~~
## .IS8 0.060 0.041 1.470 0.141
## .IS2 0.036 0.029 1.236 0.216
## .Cur_salar -0.025 0.030 -0.831 0.406
## .IS8 ~~
## .IS2 0.122 0.048 2.523 0.012
## .Cur_salar 0.078 0.049 1.589 0.112
## .IS2 ~~
## .Cur_salar 0.041 0.035 1.178 0.239
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .PA3 0.320 0.025 12.961 0.000
## .SA1 0.422 0.033 12.961 0.000
## .GA3 0.457 0.035 12.961 0.000
## .IS8 1.232 0.095 12.961 0.000
## .IS2 0.624 0.048 12.961 0.000
## .Cur_salar 0.654 0.050 12.961 0.000semPaths(fit, intercept = FALSE, whatLabel = "est", residuals = FALSE, exoCov = FALSE, layout = 'tree')
#Confirmatory Factor Analysis
We have tried few models in this part, first we construct our CFA model with all variables, we did no get a good fit, so we tried to reduces teh items for every factor.
##Model1: Four Factors wih all items
###########################################################################
# Experiment with the factors that have the lowest measure of uniqueness
###########################################################################
m1a<- 'Program Quality =~ PA1+PA2+PA3+PA4+PA5+PA6+PA7+PA8+PA9+PA10+PA11+PA12+PA13+PA14+GA1+GA2+GA3+GA4
Faculty Assistance =~ SA1+SA2+SA3+SA4+SA5+SA6+SA7+SA8+SA9+SA10+SA11+SA12+SA13
Student Satisfaction =~ IS1+IS2+IS3+IS4+IS5+IS6+IS7+IS8+IS9+IS10+IS11+IS12
Current Employmentn=~ sector_work_class+Career_day+Career_day_help+Relation+Cur_salar'
fourfac_all_items<- cfa(m1a, data=df, std.lv=TRUE)
summary(fourfac_all_items, fit.measures=TRUE)## lavaan 0.6-7 ended normally after 42 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 102
##
## Number of observations 336
##
## Model Test User Model:
##
## Test statistic 3295.884
## Degrees of freedom 1074
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 10507.455
## Degrees of freedom 1128
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.763
## Tucker-Lewis Index (TLI) 0.751
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -18651.938
## Loglikelihood unrestricted model (H1) -17003.996
##
## Akaike (AIC) 37507.875
## Bayesian (BIC) 37897.221
## Sample-size adjusted Bayesian (BIC) 37573.664
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.078
## 90 Percent confidence interval - lower 0.075
## 90 Percent confidence interval - upper 0.082
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.079
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## ProgramQuality =~
## PA1 0.686 0.046 14.955 0.000
## PA2 0.699 0.044 15.734 0.000
## PA3 0.677 0.045 15.017 0.000
## PA4 0.668 0.046 14.523 0.000
## PA5 0.786 0.051 15.561 0.000
## PA6 0.710 0.049 14.442 0.000
## PA7 0.738 0.047 15.700 0.000
## PA8 0.753 0.056 13.345 0.000
## PA9 0.746 0.048 15.520 0.000
## PA10 0.789 0.055 14.335 0.000
## PA11 0.739 0.051 14.567 0.000
## PA12 0.827 0.056 14.894 0.000
## PA13 0.704 0.055 12.706 0.000
## PA14 0.721 0.074 9.690 0.000
## GA1 0.604 0.046 13.258 0.000
## GA2 0.615 0.053 11.598 0.000
## GA3 0.562 0.049 11.539 0.000
## GA4 0.620 0.062 10.026 0.000
## FacultyAssistance =~
## SA1 0.756 0.045 16.655 0.000
## SA2 0.790 0.044 17.899 0.000
## SA3 0.821 0.045 18.266 0.000
## SA4 0.694 0.044 15.612 0.000
## SA5 0.705 0.046 15.433 0.000
## SA6 0.678 0.044 15.294 0.000
## SA7 0.682 0.043 15.994 0.000
## SA8 0.727 0.050 14.527 0.000
## SA9 0.682 0.047 14.472 0.000
## SA10 0.635 0.047 13.389 0.000
## SA11 0.646 0.049 13.151 0.000
## SA12 0.754 0.050 14.992 0.000
## SA13 0.782 0.046 16.841 0.000
## StudentSatisfaction =~
## IS1 0.655 0.061 10.705 0.000
## IS2 0.715 0.050 14.201 0.000
## IS3 0.772 0.056 13.769 0.000
## IS4 0.746 0.056 13.325 0.000
## IS5 0.633 0.047 13.455 0.000
## IS6 0.575 0.052 10.956 0.000
## IS7 0.656 0.049 13.402 0.000
## IS8 0.816 0.067 12.222 0.000
## IS9 0.419 0.046 9.078 0.000
## IS10 0.557 0.058 9.637 0.000
## IS11 0.605 0.054 11.169 0.000
## IS12 0.668 0.076 8.765 0.000
## CurrentEmploymentn =~
## sectr_wrk_clss 0.058 0.022 2.653 0.008
## Career_day -0.042 0.025 -1.669 0.095
## Career_day_hlp -0.352 0.027 -12.897 0.000
## Relation 0.309 0.025 12.412 0.000
## Cur_salar -0.929 0.060 -15.503 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## ProgramQuality ~~
## FacultyAssstnc 0.721 0.030 24.261 0.000
## StudentStsfctn 0.552 0.043 12.708 0.000
## CrrntEmplymntn -0.072 0.062 -1.161 0.245
## FacultyAssistance ~~
## StudentStsfctn 0.664 0.036 18.437 0.000
## CrrntEmplymntn -0.038 0.062 -0.607 0.544
## StudentSatisfaction ~~
## CrrntEmplymntn -0.090 0.064 -1.400 0.161
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .PA1 0.443 0.036 12.145 0.000
## .PA2 0.393 0.033 12.005 0.000
## .PA3 0.426 0.035 12.135 0.000
## .PA4 0.458 0.038 12.213 0.000
## .PA5 0.515 0.043 12.038 0.000
## .PA6 0.526 0.043 12.225 0.000
## .PA7 0.440 0.037 12.012 0.000
## .PA8 0.740 0.060 12.372 0.000
## .PA9 0.467 0.039 12.046 0.000
## .PA10 0.663 0.054 12.241 0.000
## .PA11 0.556 0.046 12.206 0.000
## .PA12 0.652 0.054 12.155 0.000
## .PA13 0.737 0.059 12.445 0.000
## .PA14 1.508 0.119 12.697 0.000
## .GA1 0.485 0.039 12.383 0.000
## .GA2 0.711 0.057 12.553 0.000
## .GA3 0.601 0.048 12.559 0.000
## .GA4 1.029 0.081 12.675 0.000
## .SA1 0.382 0.032 11.871 0.000
## .SA2 0.321 0.028 11.544 0.000
## .SA3 0.320 0.028 11.425 0.000
## .SA4 0.398 0.033 12.081 0.000
## .SA5 0.426 0.035 12.112 0.000
## .SA6 0.406 0.033 12.136 0.000
## .SA7 0.356 0.030 12.010 0.000
## .SA8 0.544 0.044 12.254 0.000
## .SA9 0.483 0.039 12.262 0.000
## .SA10 0.523 0.042 12.400 0.000
## .SA11 0.569 0.046 12.427 0.000
## .SA12 0.533 0.044 12.185 0.000
## .SA13 0.394 0.033 11.829 0.000
## .IS1 0.922 0.075 12.228 0.000
## .IS2 0.520 0.046 11.406 0.000
## .IS3 0.663 0.057 11.540 0.000
## .IS4 0.678 0.058 11.666 0.000
## .IS5 0.475 0.041 11.630 0.000
## .IS6 0.670 0.055 12.185 0.000
## .IS7 0.516 0.044 11.645 0.000
## .IS8 1.024 0.086 11.936 0.000
## .IS9 0.556 0.045 12.465 0.000
## .IS10 0.856 0.069 12.391 0.000
## .IS11 0.707 0.058 12.147 0.000
## .IS12 1.531 0.122 12.503 0.000
## .sectr_wrk_clss 0.130 0.010 12.883 0.000
## .Career_day 0.172 0.013 12.931 0.000
## .Career_day_hlp 0.126 0.014 9.250 0.000
## .Relation 0.112 0.011 9.860 0.000
## .Cur_salar 0.350 0.071 4.911 0.000
## ProgramQuality 1.000
## FacultyAssstnc 1.000
## StudentStsfctn 1.000
## CrrntEmplymntn 1.000semPaths(fourfac_all_items, intercept = FALSE, whatLabel = "est", residuals = FALSE, exoCov = FALSE, layout = 'tree')
#Model 2 Estimation and results
m1<- 'Program Quality =~ PA2+PA5+PA7+PA12
Faculty Assistance =~ SA1+SA2+SA3+SA13
Student Satisfaction =~ IS2+IS3+IS4
Current Employment =~ Career_day_help+Relation+Cur_salar'
fourfactor<- cfa(m1, data=df, std.lv=TRUE)
summary(fourfactor, fit.measures=TRUE)## lavaan 0.6-7 ended normally after 29 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 34
##
## Number of observations 336
##
## Model Test User Model:
##
## Test statistic 156.230
## Degrees of freedom 71
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 2165.984
## Degrees of freedom 91
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.959
## Tucker-Lewis Index (TLI) 0.947
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5312.561
## Loglikelihood unrestricted model (H1) -5234.446
##
## Akaike (AIC) 10693.122
## Bayesian (BIC) 10822.904
## Sample-size adjusted Bayesian (BIC) 10715.052
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.060
## 90 Percent confidence interval - lower 0.047
## 90 Percent confidence interval - upper 0.072
## P-value RMSEA <= 0.05 0.099
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.052
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## ProgramQuality =~
## PA2 0.652 0.048 13.575 0.000
## PA5 0.853 0.052 16.455 0.000
## PA7 0.771 0.049 15.783 0.000
## PA12 0.831 0.058 14.208 0.000
## FacultyAssistance =~
## SA1 0.801 0.045 17.677 0.000
## SA2 0.821 0.044 18.497 0.000
## SA3 0.841 0.046 18.440 0.000
## SA13 0.741 0.049 15.220 0.000
## StudentSatisfaction =~
## IS2 0.773 0.053 14.470 0.000
## IS3 0.839 0.059 14.180 0.000
## IS4 0.813 0.059 13.817 0.000
## CurrentEmployment =~
## Career_day_hlp 0.345 0.027 12.604 0.000
## Relation -0.313 0.025 -12.516 0.000
## Cur_salar 0.933 0.061 15.416 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## ProgramQuality ~~
## FacultyAssstnc 0.614 0.043 14.333 0.000
## StudentStsfctn 0.359 0.060 5.978 0.000
## CurrntEmplymnt 0.031 0.066 0.468 0.640
## FacultyAssistance ~~
## StudentStsfctn 0.519 0.051 10.246 0.000
## CurrntEmplymnt 0.047 0.064 0.729 0.466
## StudentSatisfaction ~~
## CurrntEmplymnt 0.082 0.068 1.212 0.226
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .PA2 0.456 0.042 10.831 0.000
## .PA5 0.406 0.046 8.812 0.000
## .PA7 0.390 0.041 9.421 0.000
## .PA12 0.646 0.061 10.505 0.000
## .SA1 0.313 0.032 9.857 0.000
## .SA2 0.271 0.029 9.173 0.000
## .SA3 0.288 0.031 9.226 0.000
## .SA13 0.456 0.041 11.166 0.000
## .IS2 0.434 0.052 8.311 0.000
## .IS3 0.555 0.064 8.670 0.000
## .IS4 0.574 0.063 9.090 0.000
## .Career_day_hlp 0.130 0.014 9.470 0.000
## .Relation 0.110 0.011 9.586 0.000
## .Cur_salar 0.342 0.073 4.660 0.000
## ProgramQuality 1.000
## FacultyAssstnc 1.000
## StudentStsfctn 1.000
## CurrntEmplymnt 1.000#Model 3 Estimation and results
m2<- 'Program Quality =~ PA1+PA2+PA3+PA4+PA5+PA6+PA7+PA9+PA11+PA12
Faculty Assistance =~ SA1+SA2+SA3+SA13
Student Satisfaction =~ IS1+IS2++IS4+IS5+IS6
Current Employment =~ Career_day_help+Relation+Cur_salar'
fourfactor_1<- cfa(m2, data=df, std.lv=TRUE)
summary(fourfactor_1, fit.measures=TRUE)## lavaan 0.6-7 ended normally after 29 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 50
##
## Number of observations 336
##
## Model Test User Model:
##
## Test statistic 596.885
## Degrees of freedom 203
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 4083.082
## Degrees of freedom 231
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.898
## Tucker-Lewis Index (TLI) 0.884
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -8350.692
## Loglikelihood unrestricted model (H1) -8052.249
##
## Akaike (AIC) 16801.384
## Bayesian (BIC) 16992.239
## Sample-size adjusted Bayesian (BIC) 16833.633
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.076
## 90 Percent confidence interval - lower 0.069
## 90 Percent confidence interval - upper 0.083
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.059
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## ProgramQuality =~
## PA1 0.700 0.046 15.264 0.000
## PA2 0.709 0.044 15.939 0.000
## PA3 0.693 0.045 15.377 0.000
## PA4 0.703 0.046 15.446 0.000
## PA5 0.816 0.050 16.277 0.000
## PA6 0.735 0.049 15.028 0.000
## PA7 0.768 0.047 16.516 0.000
## PA9 0.734 0.049 15.058 0.000
## PA11 0.715 0.052 13.814 0.000
## PA12 0.821 0.056 14.624 0.000
## FacultyAssistance =~
## SA1 0.801 0.045 17.719 0.000
## SA2 0.819 0.044 18.453 0.000
## SA3 0.842 0.045 18.512 0.000
## SA13 0.741 0.049 15.224 0.000
## StudentSatisfaction =~
## IS1 0.612 0.064 9.497 0.000
## IS2 0.622 0.055 11.373 0.000
## IS4 0.703 0.059 11.837 0.000
## IS5 0.733 0.047 15.559 0.000
## IS6 0.701 0.052 13.482 0.000
## CurrentEmployment =~
## Career_day_hlp 0.347 0.027 12.678 0.000
## Relation -0.313 0.025 -12.525 0.000
## Cur_salar 0.929 0.060 15.369 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## ProgramQuality ~~
## FacultyAssstnc 0.640 0.038 16.827 0.000
## StudentStsfctn 0.562 0.046 12.132 0.000
## CurrntEmplymnt 0.063 0.063 0.999 0.318
## FacultyAssistance ~~
## StudentStsfctn 0.604 0.045 13.435 0.000
## CurrntEmplymnt 0.047 0.064 0.732 0.464
## StudentSatisfaction ~~
## CurrntEmplymnt 0.062 0.067 0.916 0.360
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .PA1 0.423 0.036 11.765 0.000
## .PA2 0.378 0.033 11.587 0.000
## .PA3 0.405 0.034 11.737 0.000
## .PA4 0.411 0.035 11.720 0.000
## .PA5 0.467 0.041 11.488 0.000
## .PA6 0.489 0.041 11.821 0.000
## .PA7 0.394 0.035 11.413 0.000
## .PA9 0.485 0.041 11.814 0.000
## .PA11 0.592 0.049 12.071 0.000
## .PA12 0.662 0.056 11.911 0.000
## .SA1 0.312 0.032 9.891 0.000
## .SA2 0.274 0.029 9.295 0.000
## .SA3 0.285 0.031 9.241 0.000
## .SA13 0.457 0.041 11.198 0.000
## .IS1 0.976 0.082 11.921 0.000
## .IS2 0.644 0.057 11.321 0.000
## .IS4 0.741 0.067 11.133 0.000
## .IS5 0.340 0.039 8.604 0.000
## .IS6 0.508 0.049 10.281 0.000
## .Career_day_hlp 0.129 0.014 9.388 0.000
## .Relation 0.110 0.011 9.593 0.000
## .Cur_salar 0.349 0.073 4.778 0.000
## ProgramQuality 1.000
## FacultyAssstnc 1.000
## StudentStsfctn 1.000
## CurrntEmplymnt 1.000#Model 4 Estimation and results
m3<- 'Program Quality =~ PA2+PA5+PA7+PA12
Faculty Assistance =~ SA1+SA2+SA3+SA13
Student Satisfaction =~ IS2+IS4
Current Employment =~ Career_day_help+Relation+Cur_salar'
fourfactor_2<- cfa(m3, data=df, std.lv=TRUE)
summary(fourfactor_2, fit.measures=TRUE)## lavaan 0.6-7 ended normally after 32 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 32
##
## Number of observations 336
##
## Model Test User Model:
##
## Test statistic 120.085
## Degrees of freedom 59
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1951.936
## Degrees of freedom 78
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.967
## Tucker-Lewis Index (TLI) 0.957
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4886.066
## Loglikelihood unrestricted model (H1) -4826.024
##
## Akaike (AIC) 9836.133
## Bayesian (BIC) 9958.280
## Sample-size adjusted Bayesian (BIC) 9856.772
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.056
## 90 Percent confidence interval - lower 0.041
## 90 Percent confidence interval - upper 0.070
## P-value RMSEA <= 0.05 0.249
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.047
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## ProgramQuality =~
## PA2 0.652 0.048 13.586 0.000
## PA5 0.853 0.052 16.472 0.000
## PA7 0.770 0.049 15.774 0.000
## PA12 0.830 0.058 14.191 0.000
## FacultyAssistance =~
## SA1 0.800 0.045 17.668 0.000
## SA2 0.821 0.044 18.528 0.000
## SA3 0.841 0.046 18.476 0.000
## SA13 0.740 0.049 15.176 0.000
## StudentSatisfaction =~
## IS2 0.759 0.065 11.672 0.000
## IS4 0.787 0.070 11.215 0.000
## CurrentEmployment =~
## Career_day_hlp 0.345 0.027 12.598 0.000
## Relation -0.312 0.025 -12.498 0.000
## Cur_salar 0.934 0.061 15.428 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## ProgramQuality ~~
## FacultyAssstnc 0.614 0.043 14.327 0.000
## StudentStsfctn 0.407 0.063 6.447 0.000
## CurrntEmplymnt 0.031 0.066 0.466 0.641
## FacultyAssistance ~~
## StudentStsfctn 0.579 0.053 10.934 0.000
## CurrntEmplymnt 0.047 0.064 0.733 0.464
## StudentSatisfaction ~~
## CurrntEmplymnt 0.089 0.072 1.237 0.216
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .PA2 0.456 0.042 10.827 0.000
## .PA5 0.405 0.046 8.799 0.000
## .PA7 0.391 0.041 9.432 0.000
## .PA12 0.647 0.062 10.517 0.000
## .SA1 0.314 0.032 9.881 0.000
## .SA2 0.269 0.029 9.166 0.000
## .SA3 0.286 0.031 9.214 0.000
## .SA13 0.459 0.041 11.192 0.000
## .IS2 0.454 0.077 5.918 0.000
## .IS4 0.615 0.087 7.039 0.000
## .Career_day_hlp 0.130 0.014 9.471 0.000
## .Relation 0.110 0.011 9.604 0.000
## .Cur_salar 0.340 0.074 4.627 0.000
## ProgramQuality 1.000
## FacultyAssstnc 1.000
## StudentStsfctn 1.000
## CurrntEmplymnt 1.000Model 5 Estimation and results
m4<- 'Program Quality =~ PA2+PA5+PA7+PA12
Faculty Assistance =~ SA1+SA2+SA3+SA13
Student Satisfaction =~ IS2+IS3+IS4
Current Employment =~ Career_day+Cur_salar'
fourfactor_3<- cfa(m4, data=df, std.lv=TRUE)
summary(fourfactor_3, fit.measures=TRUE)## lavaan 0.6-7 ended normally after 62 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 32
##
## Number of observations 336
##
## Model Test User Model:
##
## Test statistic 130.979
## Degrees of freedom 59
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1869.525
## Degrees of freedom 78
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.960
## Tucker-Lewis Index (TLI) 0.947
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5174.154
## Loglikelihood unrestricted model (H1) -5108.664
##
## Akaike (AIC) 10412.307
## Bayesian (BIC) 10534.455
## Sample-size adjusted Bayesian (BIC) 10432.947
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.060
## 90 Percent confidence interval - lower 0.046
## 90 Percent confidence interval - upper 0.074
## P-value RMSEA <= 0.05 0.108
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.050
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## ProgramQuality =~
## PA2 0.649 0.048 13.504 0.000
## PA5 0.855 0.052 16.531 0.000
## PA7 0.769 0.049 15.730 0.000
## PA12 0.833 0.058 14.269 0.000
## FacultyAssistance =~
## SA1 0.801 0.045 17.678 0.000
## SA2 0.821 0.044 18.503 0.000
## SA3 0.840 0.046 18.428 0.000
## SA13 0.742 0.049 15.228 0.000
## StudentSatisfaction =~
## IS2 0.776 0.053 14.578 0.000
## IS3 0.837 0.059 14.164 0.000
## IS4 0.811 0.059 13.822 0.000
## CurrentEmployment =~
## Career_day 0.252 0.114 2.219 0.026
## Cur_salar 0.180 0.099 1.805 0.071
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## ProgramQuality ~~
## FacultyAssstnc 0.614 0.043 14.331 0.000
## StudentStsfctn 0.360 0.060 6.000 0.000
## CurrntEmplymnt 0.299 0.154 1.944 0.052
## FacultyAssistance ~~
## StudentStsfctn 0.520 0.051 10.267 0.000
## CurrntEmplymnt 0.285 0.148 1.928 0.054
## StudentSatisfaction ~~
## CurrntEmplymnt 0.400 0.188 2.122 0.034
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .PA2 0.460 0.042 10.874 0.000
## .PA5 0.402 0.046 8.758 0.000
## .PA7 0.393 0.041 9.482 0.000
## .PA12 0.642 0.061 10.483 0.000
## .SA1 0.313 0.032 9.857 0.000
## .SA2 0.270 0.029 9.168 0.000
## .SA3 0.288 0.031 9.238 0.000
## .SA13 0.456 0.041 11.163 0.000
## .IS2 0.429 0.052 8.283 0.000
## .IS3 0.559 0.064 8.784 0.000
## .IS4 0.576 0.063 9.164 0.000
## .Career_day 0.110 0.057 1.929 0.054
## .Cur_salar 1.180 0.095 12.367 0.000
## ProgramQuality 1.000
## FacultyAssstnc 1.000
## StudentStsfctn 1.000
## CurrntEmplymnt 1.000Model 6 Estimation and results
m5<- 'Program Quality =~ PA2+PA5+PA7+PA12
Faculty Assistance =~ SA1+SA2+SA3+SA13
Student Satisfaction =~ IS2+IS3+IS4
Current Employment =~ Relation+Cur_salar'
fourfactor_4<- cfa(m5, data=df, std.lv=TRUE)
summary(fourfactor_4, fit.measures=TRUE)## lavaan 0.6-7 ended normally after 56 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 32
##
## Number of observations 336
##
## Model Test User Model:
##
## Test statistic 132.930
## Degrees of freedom 59
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1987.909
## Degrees of freedom 78
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.961
## Tucker-Lewis Index (TLI) 0.949
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5146.374
## Loglikelihood unrestricted model (H1) -5079.909
##
## Akaike (AIC) 10356.749
## Bayesian (BIC) 10478.896
## Sample-size adjusted Bayesian (BIC) 10377.389
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.061
## 90 Percent confidence interval - lower 0.047
## 90 Percent confidence interval - upper 0.075
## P-value RMSEA <= 0.05 0.091
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.050
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## ProgramQuality =~
## PA2 0.652 0.048 13.588 0.000
## PA5 0.853 0.052 16.465 0.000
## PA7 0.770 0.049 15.762 0.000
## PA12 0.831 0.058 14.204 0.000
## FacultyAssistance =~
## SA1 0.801 0.045 17.683 0.000
## SA2 0.820 0.044 18.486 0.000
## SA3 0.840 0.046 18.435 0.000
## SA13 0.742 0.049 15.231 0.000
## StudentSatisfaction =~
## IS2 0.773 0.053 14.473 0.000
## IS3 0.840 0.059 14.202 0.000
## IS4 0.812 0.059 13.810 0.000
## CurrentEmployment =~
## Relation 0.351 0.122 2.875 0.004
## Cur_salar -0.832 0.290 -2.873 0.004
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## ProgramQuality ~~
## FacultyAssstnc 0.614 0.043 14.342 0.000
## StudentStsfctn 0.359 0.060 5.978 0.000
## CurrntEmplymnt 0.022 0.069 0.316 0.752
## FacultyAssistance ~~
## StudentStsfctn 0.519 0.051 10.243 0.000
## CurrntEmplymnt -0.007 0.067 -0.097 0.923
## StudentSatisfaction ~~
## CurrntEmplymnt -0.093 0.071 -1.302 0.193
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .PA2 0.456 0.042 10.825 0.000
## .PA5 0.406 0.046 8.803 0.000
## .PA7 0.391 0.041 9.439 0.000
## .PA12 0.646 0.062 10.508 0.000
## .SA1 0.313 0.032 9.851 0.000
## .SA2 0.271 0.030 9.182 0.000
## .SA3 0.288 0.031 9.229 0.000
## .SA13 0.456 0.041 11.161 0.000
## .IS2 0.434 0.052 8.323 0.000
## .IS3 0.553 0.064 8.659 0.000
## .IS4 0.575 0.063 9.110 0.000
## .Relation 0.085 0.085 1.004 0.315
## .Cur_salar 0.521 0.476 1.094 0.274
## ProgramQuality 1.000
## FacultyAssstnc 1.000
## StudentStsfctn 1.000
## CurrntEmplymnt 1.000semPaths(fourfactor_4, intercept = FALSE, whatLabel = "est", residuals = FALSE, exoCov = FALSE, layout = 'tree')