Factor loadings when latent variable only has a single indicator variable

[RMH]

I have built an SEM that includes two factors with single indicator variables:

FactorA =~ IndicatorA

FactorB =~ IndicatorB

I know I should be able to include IndicatorA and IndicatorB directly in the model, but that was causing problems with the multigroup analysis. I will save that issue for a separate post.

My question is:

Shouldn't the factor loadings (both standardized and unstandardized) be 1 when there is only one indicator?  

The output I get for this model includes (this is only the output for these two variables):

Latent Variables:

                                          Estimate  Std.Err  Z-value  P(>|z|)   Std.lv  Std.all

 FactorA =~ IndicatorA         0.535    0.009   58.706    0.000    1.341    1.000

  FactorB =~ IndicatorB        0.946    0.009  106.475    0.000    1.070    1.000

Why are the estimates not 1?

Thanks!

RMH

[Edward Rigdon]

     Fixing the loading at 1 (or some other nonzero constant) is necessary if the variance of the factor is free to be estimated. If your syntax fixed the variance of the factor (at 1, say), then there is no need to fix the loading at 1. So it depends on the rest of your syntax and the specific function (lavaan or sem / cfa) that you used.

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[RMH]

Thanks Edward! I fixed the variance of the factors to be 1 using the option std.lv=TRUE in the sem function. So you are saying under this condition, that the the factor loading would not have to be 1?

[Edward Rigdon]

     Yes,exactly.  If your data are not themselves standardized, then a standardized factors and a loading fixed to 1 would probably be inconsistent constraints.

--

[Yves Rosseel]

If you omit the std.lv= argument (or set it to FALSE), you will get 1.0
for both factor loadings (but now the factor variances will be estimated).

Yves.

On 07/08/2016 02:30 AM, Edward Rigdon wrote:
> Yes,exactly. If your data are not themselves standardized, then a
> standardized factors and a loading fixed to 1 would probably be
> inconsistent constraints.
>
> On Thu, Jul 7, 2016 at 5:58 PM, RMH <robyn...@gmail.com
> <mailto:robyn...@gmail.com>> wrote:
>
> Thanks Edward! I fixed the variance of the factors to be 1 using the

> option std.lv <http://std.lv>=TRUE in the sem function. So you are

> <mailto:lavaan+un...@googlegroups.com>.

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