[R] Results of CFA with Lavaan

R Help rhelp.stats at gmail.com
Wed Jun 8 22:14:50 CEST 2011


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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