interpretation

[Dr. Hans Hansen]

Dear Yves and my fellow lavaan-users,

could someone explain to me how to interpret thresholds and latent variable estimates in a CFA where i impose a unidimensional model over some likert-items with 5 categories?

Please note, that i standardized ov and lv. So, it seems that item_001 has a very high loading, but is this still a correlation between item_001 and myFactor?
And can i make sense of the thresholds? what do they tell me?

eg:

Latent variables:
  myFactor =~
    item_001           0.913    0.004  204.134    0.000
...

Thresholds:
    
    item_001|t1        0.447    0.021   21.124    0.000
    item_001|t2        0.915    0.024   38.436    0.000
    item_001|t3        1.454    0.031   47.651    0.000
    item_001|t4        2.155    0.051   41.873    0.000
...

And, finally: to what extend does it matter to estimate a unidimensional model with WLMSV estimator AND ordered categories. How does it compare to estimate such a model with only using WLMSV and not specifying ordered responses?

Thanks a lot,
Hans

[Mauricio Garnier-Villarreal]

Hi Hans

The interpretation of the factor loadings doesnt change by analizing categorical data.

Each threshold is the score in the latent variable needed for a subject to change answer one category over the other.

From your example:

Thresholds:
    
    item_001|t1        0.447    0.021   21.124    0.000
    item_001|t2        0.915    0.024   38.436    0.000
    item_001|t3        1.454    0.031   47.651    0.000
    item_001|t4        2.155    0.051   41.873    0.000

A subject with a score in the latent variable lower than .447 is most likely to answer the first category.
A subject with a score in the latent variable higher that .447 and lower than .915 is most likely to answer the second category.
A subject with a score in the latent variable higher than .915 and lower than 1.454 is most likely to answer the third category
A subject with a score in the latent variable higher than 1.454 and lower than 2.155 is most liekly to answer the fourth category
A subject with a score in the latent variable higher than 2.155 is most likely to answer the fifth category

Hope this help

-- Mauricio

[Dr. Hans Hansen]

Thanks! So, this sounds very similar to an IRT-model then? Is it a specific one like the General Partial Credit Model or the Graded Response Model? Would it be possible to plot Item Characteristic Functions from these parameters?

And would only using WLMSV and not specifying ordered responses imply that there is a linear relationship between the response and the latent variable? Can this relation be plotted?

thanks a lot, hans

[Edward Rigdon]

     The thresholds are z scores--points on the standard normal distribution--, so they tell you something about the distribution of responses across response categories.  The first threshold of .447, being positive, tells you that more than half of all respondents replied in the first response category.  in other words, the distribution is highly skewed.

--Ed Rigdon

Sent from my iPad

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[yrosseel]

On 11/22/2013 12:37 PM, Dr. Hans Hansen wrote:
>
> Thanks! So, this sounds very similar to an IRT-model then?

Yes, there is a close connection. Currently, lavaan only provides a
WLS(MV) estimator, while IRT traditionally uses (Marginal) ML, so there
will be some small differences in the parameter estimates. But a large
family of IRT models can be fitted using SEM software.

A (very short) discussion with some references can be found in this
document:

http://users.ugent.be/~yrosseel/lavaan/jena2013.pdf

See section 3.6, and pages 101 and 102 in particular.

Yves.

[Dr. Hans Hansen]

Great, thanks a lot. 

I am still curious about the difference in using WLSMV with and without ordered responses, though. 

[yrosseel]

AFAIK, there is some literature on WLS for continuous data (bottom line:
works great, but you need a huge sample size), but not on WLSMV (which
is DWLS + mean/var-adjusted test statistic) for continuous data.

Yves.