[R] Results of CFA with Lavaan

[John Fox]

Dear Sam,

In each case, the first observed variable is treated as a "reference
indicator" with its coefficient fixed to 1 to establish the metric of the
corresponding factor and therefore to identify the model. If you didn't do
the same thing (or something equivalent, such as fixing the factor variances
to 1) in specifying the model to sem::sem(), that might account for the
problems you encountered.

Best,
 John

--------------------------------
John Fox
Senator William McMaster
  Professor of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
http://socserv.mcmaster.ca/jfox

 

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
> On Behalf Of R Help
> Sent: June-08-11 4:15 PM
> To: r-help
> Subject: [R] Results of CFA with Lavaan
> 
> 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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