PSYC214_Lab8
Chelsea McElwee
2023-05-26
Set up environment
library(psych)
library(lavaan)## This is lavaan 0.6-15
## lavaan is FREE software! Please report any bugs.##
## Attaching package: 'lavaan'## The following object is masked from 'package:psych':
##
## cor2covImport data and set up correlation matrix with variable names
CorrMat <- matrix(scan(file='child_obs.dat'),ncol=8)
colnames(CorrMat) <- c("cry","fear","soc","activ","verbal","ease","socinv","expl")
rownames(CorrMat) <- c("cry","fear","soc","activ","verbal","ease","socinv","expl")
CorrMat## cry fear soc activ verbal ease socinv expl
## cry 1.00 0.71 0.52 0.63 -0.05 0.00 -0.05 -0.04
## fear 0.71 1.00 0.50 0.55 -0.04 -0.01 -0.07 -0.07
## soc 0.52 0.50 1.00 0.48 -0.14 -0.14 -0.05 -0.18
## activ 0.63 0.55 0.48 1.00 -0.03 0.02 0.00 0.03
## verbal -0.05 -0.04 -0.14 -0.03 1.00 0.66 0.40 0.37
## ease 0.00 -0.01 -0.14 0.02 0.66 1.00 0.42 0.55
## socinv -0.05 -0.07 -0.05 0.00 0.40 0.42 1.00 0.53
## expl -0.04 -0.07 -0.18 0.03 0.37 0.55 0.53 1.00Let’s examine the correlation matrix. Based on the pattern of correlations, what do you think will happen will happen when we extract factors? How many factors do you think we’ll be able to extract only based on the patterns in the correlation matrix?
Extracting Factors
Let’s use the psych package to try to figure out how many factors to extract based on our correlation matrix. We will use different methods: Eigenvalues & eigenvectors; scree plots, parallel test
#eigenvalues
eigen(CorrMat)## eigen() decomposition
## $values
## [1] 2.8198845 2.3766540 0.7507196 0.6066356 0.4590880 0.4277279 0.2853157
## [8] 0.2739745
##
## $vectors
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -0.4521422 0.2903285 -0.06214806 0.19392934 0.259405970 -0.0279186
## [2,] -0.4410647 0.2672811 -0.14042664 0.14646920 0.568429409 0.1444129
## [3,] -0.4280631 0.1513488 0.15178101 -0.66625332 -0.320472813 0.4677588
## [4,] -0.3998511 0.2993952 0.08605121 0.23719307 -0.581094047 -0.5452557
## [5,] 0.2601046 0.4155417 -0.55611565 -0.30901941 0.001160685 -0.2408235
## [6,] 0.2584873 0.4748983 -0.35306557 0.05924143 -0.164277521 0.2776815
## [7,] 0.2342350 0.3973416 0.58271245 -0.38073760 0.344654050 -0.3774149
## [8,] 0.2618668 0.4190972 0.41533358 0.44364455 -0.153129257 0.4297888
## [,7] [,8]
## [1,] 0.35053664 0.69199634
## [2,] -0.29371965 -0.51245636
## [3,] -0.06717184 0.03018887
## [4,] -0.05892183 -0.21993265
## [5,] -0.47685822 0.26367022
## [6,] 0.61268959 -0.31624102
## [7,] 0.18213273 -0.09131238
## [8,] -0.38329410 0.17714258#scree plot
scree(CorrMat, hline=TRUE, factors=FALSE)
#parallel analysis
fa.parallel(CorrMat,n.obs=453)
## Parallel analysis suggests that the number of factors = 2 and the number of components = 2# minimum average partial
nfactors(CorrMat,n.obs=453)$map
## [1] 0.14260361 0.06232114 0.10484149 0.17446582 0.27767585 0.46714201 1.00000000
## [8] NAVectors. For each column, if you square the value and add them up, they should add up to the eigenvalues at the top. We only have 2 eigenvalues that are greater than 1; therefore, we can support extracting 2 factors given our correlation matrix.
Parallel analysis suggests the same thing, as well as scree plot
FACTOR ANALYSIS USING PSYCH PACKAGE
EFA with no rotation
fa(CorrMat,n.obs=453, nfactors=2, rotate="none", fm="pa")## Factor Analysis using method = pa
## Call: fa(r = CorrMat, nfactors = 2, n.obs = 453, rotate = "none", fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 h2 u2 com
## cry 0.79 0.37 0.76 0.24 1.4
## fear 0.73 0.32 0.63 0.37 1.4
## soc 0.63 0.13 0.42 0.58 1.1
## activ 0.64 0.35 0.53 0.47 1.5
## verbal -0.34 0.60 0.47 0.53 1.6
## ease -0.36 0.75 0.70 0.30 1.4
## socinv -0.29 0.52 0.36 0.64 1.6
## expl -0.34 0.59 0.46 0.54 1.6
##
## PA1 PA2
## SS loadings 2.40 1.92
## Proportion Var 0.30 0.24
## Cumulative Var 0.30 0.54
## Proportion Explained 0.55 0.45
## Cumulative Proportion 0.55 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 2 factors are sufficient.
##
## df null model = 28 with the objective function = 3.06 with Chi Square = 1372.78
## df of the model are 13 and the objective function was 0.21
##
## The root mean square of the residuals (RMSR) is 0.04
## The df corrected root mean square of the residuals is 0.06
##
## The harmonic n.obs is 453 with the empirical chi square 46.72 with prob < 1.1e-05
## The total n.obs was 453 with Likelihood Chi Square = 93.39 with prob < 3.1e-14
##
## Tucker Lewis Index of factoring reliability = 0.871
## RMSEA index = 0.117 and the 90 % confidence intervals are 0.095 0.14
## BIC = 13.88
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1 PA2
## Correlation of (regression) scores with factors 0.93 0.91
## Multiple R square of scores with factors 0.87 0.82
## Minimum correlation of possible factor scores 0.73 0.65What do you notice?
EFA using varimax rotation
#commonly loading and h2 is the variance for the item # adopt and closer to simple structure
fa(CorrMat,n.obs=453, nfactors=2, rotate="varimax", fm="pa")## Factor Analysis using method = pa
## Call: fa(r = CorrMat, nfactors = 2, n.obs = 453, rotate = "varimax",
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 h2 u2 com
## cry 0.87 0.00 0.76 0.24 1.0
## fear 0.79 -0.02 0.63 0.37 1.0
## soc 0.63 -0.15 0.42 0.58 1.1
## activ 0.72 0.04 0.53 0.47 1.0
## verbal -0.05 0.68 0.47 0.53 1.0
## ease -0.01 0.84 0.70 0.30 1.0
## socinv -0.04 0.60 0.36 0.64 1.0
## expl -0.05 0.68 0.46 0.54 1.0
##
## PA1 PA2
## SS loadings 2.31 2.01
## Proportion Var 0.29 0.25
## Cumulative Var 0.29 0.54
## Proportion Explained 0.53 0.47
## Cumulative Proportion 0.53 1.00
##
## Mean item complexity = 1
## Test of the hypothesis that 2 factors are sufficient.
##
## df null model = 28 with the objective function = 3.06 with Chi Square = 1372.78
## df of the model are 13 and the objective function was 0.21
##
## The root mean square of the residuals (RMSR) is 0.04
## The df corrected root mean square of the residuals is 0.06
##
## The harmonic n.obs is 453 with the empirical chi square 46.72 with prob < 1.1e-05
## The total n.obs was 453 with Likelihood Chi Square = 93.39 with prob < 3.1e-14
##
## Tucker Lewis Index of factoring reliability = 0.871
## RMSEA index = 0.117 and the 90 % confidence intervals are 0.095 0.14
## BIC = 13.88
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1 PA2
## Correlation of (regression) scores with factors 0.93 0.91
## Multiple R square of scores with factors 0.87 0.82
## Minimum correlation of possible factor scores 0.73 0.64What do you notice? zeros and negative
EFA using oblimin rotation
fa(CorrMat,n.obs=453, nfactors=2, rotate="oblimin", fm="pa")## Loading required namespace: GPArotation## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : I
## am sorry, to do these rotations requires the GPArotation package to be
## installed## Factor Analysis using method = pa
## Call: fa(r = CorrMat, nfactors = 2, n.obs = 453, rotate = "oblimin",
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 h2 u2 com
## cry 0.79 0.37 0.76 0.24 1.4
## fear 0.73 0.32 0.63 0.37 1.4
## soc 0.63 0.13 0.42 0.58 1.1
## activ 0.64 0.35 0.53 0.47 1.5
## verbal -0.34 0.60 0.47 0.53 1.6
## ease -0.36 0.75 0.70 0.30 1.4
## socinv -0.29 0.52 0.36 0.64 1.6
## expl -0.34 0.59 0.46 0.54 1.6
##
## PA1 PA2
## SS loadings 2.40 1.92
## Proportion Var 0.30 0.24
## Cumulative Var 0.30 0.54
## Proportion Explained 0.55 0.45
## Cumulative Proportion 0.55 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 2 factors are sufficient.
##
## df null model = 28 with the objective function = 3.06 with Chi Square = 1372.78
## df of the model are 13 and the objective function was 0.21
##
## The root mean square of the residuals (RMSR) is 0.04
## The df corrected root mean square of the residuals is 0.06
##
## The harmonic n.obs is 453 with the empirical chi square 46.72 with prob < 1.1e-05
## The total n.obs was 453 with Likelihood Chi Square = 93.39 with prob < 3.1e-14
##
## Tucker Lewis Index of factoring reliability = 0.871
## RMSEA index = 0.117 and the 90 % confidence intervals are 0.095 0.14
## BIC = 13.88
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1 PA2
## Correlation of (regression) scores with factors 0.93 0.91
## Multiple R square of scores with factors 0.87 0.82
## Minimum correlation of possible factor scores 0.73 0.65What do you notice?
similar to the intial rotation - start with the orthogonal first
EFA using Lavaan
efa_model2 <- "
efa('block1')*F1 =~ cry+fear+soc+activ+verbal+ease+socinv+expl
efa('block1')*F2 =~ cry+fear+soc+activ+verbal+ease+socinv+expl
"
efa_sat2 <- lavaan(
model = efa_model2,
sample.cov = CorrMat,
auto.var = TRUE,
auto.efa = TRUE,
sample.nobs=453,
sample.cov.rescale = FALSE)
summary(efa_sat2,fit.measures=T)## lavaan 0.6.15 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 23
##
## Rotation method GEOMIN OBLIQUE
## Geomin epsilon 0.001
## Rotation algorithm (rstarts) GPA (30)
## Standardized metric TRUE
## Row weights None
##
## Number of observations 453
##
## Model Test User Model:
##
## Test statistic 88.514
## Degrees of freedom 13
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1386.552
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.944
## Tucker-Lewis Index (TLI) 0.880
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4493.214
## Loglikelihood unrestricted model (H1) -4448.957
##
## Akaike (AIC) 9032.429
## Bayesian (BIC) 9127.094
## Sample-size adjusted Bayesian (SABIC) 9054.100
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.113
## 90 Percent confidence interval - lower 0.092
## 90 Percent confidence interval - upper 0.136
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.994
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.041
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## F1 =~ block1
## cry 0.877 0.040 21.744 0.000
## fear 0.801 0.042 19.199 0.000
## soc 0.608 0.045 13.633 0.000
## activ 0.718 0.043 16.574 0.000
## verbal -0.015 0.024 -0.614 0.539
## ease 0.043 0.030 1.468 0.142
## socinv -0.021 0.039 -0.546 0.585
## expl -0.020 0.034 -0.601 0.548
## F2 =~ block1
## cry 0.007 0.017 0.382 0.703
## fear -0.011 0.023 -0.463 0.643
## soc -0.153 0.042 -3.645 0.000
## activ 0.038 0.036 1.049 0.294
## verbal 0.727 0.045 16.181 0.000
## ease 0.872 0.043 20.073 0.000
## socinv 0.543 0.047 11.461 0.000
## expl 0.636 0.046 13.833 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .cry 0.231 0.033 7.095 0.000
## .fear 0.358 0.034 10.420 0.000
## .soc 0.597 0.044 13.512 0.000
## .activ 0.487 0.039 12.505 0.000
## .verbal 0.470 0.042 11.096 0.000
## .ease 0.243 0.042 5.721 0.000
## .socinv 0.703 0.051 13.783 0.000
## .expl 0.593 0.046 12.869 0.000
## F1 1.000
## F2 1.000