CFA on non-normal ordinal data

Question

I hope you are doing well,

I'm taking my first steps in R and the Lavaan Package, and I'm trying to investigate the factorial structure of a measure related to dating victimization. The sample consists of 957 participants without missing values. The response options use a 5-point Likert scale. Both univariate and multivariate normalities are violated.

Here is the model, along with the outputs and warning messages.

Model.

Four first-order factor structure

model <- '

f1 =~ TV1 + TV2 + TV3 + TV4 + TV5 + TV6 + TV7 + TV8 + TV9 + TV10

f2 =~ TV11 + TV12 + TV13 + TV14 + TV15 + TV16 + TV17

f3 =~ TV18 + TV19 + TV20 + TV21 + TV22+ TV23 + TV24 + TV25

f4 =~ TV26 + TV27 + TV28 + TV29+ TV30'

fit.model <- cfa(model, data = TARV, ordered = TRUE, estimator = "DWLS", se = "robust", test = "scaled.shifted", std.lv = TRUE)

summary(fit.model, std = TRUE, fit.measures = TRUE)

Output:

lavaan 0.6.16 ended normally after 34 iterations

Estimator DWLS

Optimization method NLMINB

Number of model parameters 185

Number of observations 957

Model Test User Model:

                                          Standard      Scaled

Test Statistic 381.267 617.183

Degrees of freedom 399 399

P-value (Chi-square) 0.730 0.000

Scaling correction factor 1.083

Shift parameter 265.087

simple second-order correction

Model Test Baseline Model:

Test statistic 142505.191 17287.640

Degrees of freedom 435 435

P-value 0.000 0.000

Scaling correction factor 8.430

User Model versus Baseline Model:

Comparative Fit Index (CFI) 1.000 0.987

Tucker-Lewis Index (TLI) 1.000 0.986

Robust Comparative Fit Index (CFI) NA

Robust Tucker-Lewis Index (TLI) NA

Root Mean Square Error of Approximation:

RMSEA 0.000 0.024

90 Percent confidence interval - lower 0.000 0.020

90 Percent confidence interval - upper 0.009 0.028

P-value H_0: RMSEA <= 0.050 1.000 1.000

P-value H_0: RMSEA >= 0.080 0.000 0.000

Robust RMSEA NA

90 Percent confidence interval - lower NA

90 Percent confidence interval - upper NA

P-value H_0: Robust RMSEA <= 0.050 NA

P-value H_0: Robust RMSEA >= 0.080 NA

Standardized Root Mean Square Residual:

SRMR 0.041 0.041

I am getting this warning message:

Warning message:

In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, :

lavaan WARNING:

The variance-covariance matrix of the estimated parameters (vcov)

does not appear to be positive definite! The smallest eigenvalue

(= -5.592776e-16) is smaller than zero. This may be a symptom that

the model is not identified.

I did run these functions, and I am getting these outputs:

lavInspect(fit.model, "cov.lv")

  f1    f2    f3    f4

f1 1.000

f2 0.854 1.000

f3 0.922 0.816 1.000

f4 0.903 0.873 0.937 1.000

det(lavInspect(fit.model, "cov.lv"))

[1] 0.003425802

eigen(lavInspect(fit.model, "cov.lv"))

eigen() decomposition

$values

[1] 3.6536666 0.1999477 0.0990346 0.0473511

$vectors

       [,1]       [,2]          [,3]       [,4]

[1,] -0.5036916 0.1988844 0.7828187299 0.3064875

[2,] -0.4841475 -0.8386756 -0.0007780208 -0.2494471

[3,] -0.5033330 0.4944816 -0.1812847326 -0.6850399

[4,] -0.5084800 0.1120542 -0.5952563117 0.6120146

What can I do to find out the origin of these messages and solve the problem?

Are the DWLS, robust and scaled.shifted correct for the scale type and sample size? Or should I change for MLM, robust and satorra.bentler?

Does the chi-square statistic and is p-value compromise the model?

I'm sorry if these seem like really basic questions.

Thank you,

Maria

CFA on non-normal ordinal data

Answers (1)

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