I've just found the lavaan package, and I really appreciate it, as it
seems to succeed with models that were failing in sem::sem. I need
some clarification, however, in the output, and I was hoping the list
could help me.
I'll go with the standard example from the help documentation, as my
problem is much larger but no more complicated than that.
My question is, why is there one latent estimate that is set to 1 with
no SD for each factor? Is that normal? When I've managed to get
sem::sem to fit a model this has not been the case.
Thanks,
Sam Stewart
HS.model <- ' visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9 '
fit <- sem(HS.model, data=HolzingerSwineford1939)
summary(fit, fit.measures=TRUE)
Lavaan (0.4-8) converged normally after 35 iterations
Number of observations 301
Estimator ML
Minimum Function Chi-square 85.306
Degrees of freedom 24
P-value 0.000
Chi-square test baseline model:
Minimum Function Chi-square 918.852
Degrees of freedom 36
P-value 0.000
Full model versus baseline model:
Comparative Fit Index (CFI) 0.931
Tucker-Lewis Index (TLI) 0.896
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -3737.745
Loglikelihood unrestricted model (H1) -3695.092
Number of free parameters 21
Akaike (AIC) 7517.490
Bayesian (BIC) 7595.339
Sample-size adjusted Bayesian (BIC) 7528.739
Root Mean Square Error of Approximation:
RMSEA 0.092
90 Percent Confidence Interval 0.071 0.114
P-value RMSEA <= 0.05 0.001
Standardized Root Mean Square Residual:
SRMR 0.065
Parameter estimates:
Information Expected
Standard Errors Standard
Estimate Std.err Z-value P(>|z|)
Latent variables:
visual =~
x1 1.000
x2 0.554 0.100 5.554 0.000
x3 0.729 0.109 6.685 0.000
textual =~
x4 1.000
x5 1.113 0.065 17.014 0.000
x6 0.926 0.055 16.703 0.000
speed =~
x7 1.000
x8 1.180 0.165 7.152 0.000
x9 1.082 0.151 7.155 0.000
Covariances:
visual ~~
textual 0.408 0.074 5.552 0.000
speed 0.262 0.056 4.660 0.000
textual ~~
speed 0.173 0.049 3.518 0.000
Variances:
x1 0.549 0.114 4.833 0.000
x2 1.134 0.102 11.146 0.000
x3 0.844 0.091 9.317 0.000
x4 0.371 0.048 7.778 0.000
x5 0.446 0.058 7.642 0.000
x6 0.356 0.043 8.277 0.000
x7 0.799 0.081 9.823 0.000
x8 0.488 0.074 6.573 0.000
x9 0.566 0.071 8.003 0.000
visual 0.809 0.145 5.564 0.000
textual 0.979 0.112 8.737 0.000
speed 0.384 0.086 4.451 0.000
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