# Other Longitudinal Methods (Cross-Lag, Latent Difference Score models)

## Other Longitudinal Methods (Cross-Lag, Latent Difference Score models)

Hi All!

If you have been directed to this post, you stated that you were interested in, or are currently using, longitudinal modeling methods such as cross-lagged panel models or latent difference score models in your analyses. Please use this forum to connect with each other either in person or online... It would be great if we could share knowledge and advice with each other!

If you have been directed to this post, you stated that you were interested in, or are currently using, longitudinal modeling methods such as cross-lagged panel models or latent difference score models in your analyses. Please use this forum to connect with each other either in person or online... It would be great if we could share knowledge and advice with each other!

**CatieWalsh**- Posts : 22

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Location : OEH sometimes, but mostly wandering around Sennott

## Re: Other Longitudinal Methods (Cross-Lag, Latent Difference Score models)

Hi all!

My lab does a lot of work with latent growth trajectory models and structural equation modeling in general, so I'm looking to learn just about any model in this area! I don't have any active projects using this type of modeling right now, but I'll be sure to update this if something arises!

My lab does a lot of work with latent growth trajectory models and structural equation modeling in general, so I'm looking to learn just about any model in this area! I don't have any active projects using this type of modeling right now, but I'll be sure to update this if something arises!

**kirstenmckone**- Posts : 6

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## Re: Other Longitudinal Methods (Cross-Lag, Latent Difference Score models)

Hi everyone!

I have a question about standardizing variables BEFORE running your Mplus analyses, such that the output would replicate STDYX output. I am interested in doing this to see if certain predictors are statistically stronger than others (by setting them to equivalence and seeing if model fit decreases), and want them to be standardized at the outset.

When you input the code, Mplus assumes that you are setting

My sense is that you can do this with observed variables without issues--the "unstandardized" output should almost be identical to STDYX.

However, how can you do this same trick with latent variables? I set the latent variable variances to 1, similar to standardized variables. However, when I looked this up online to see if it would be the same as STDYX, Bengt Muthen replied to someone else:

I then tried standardizing the indicators via Mplus code, but the "unstandardized" output did not replicate the STDYX output exactly.

Any help would be great!

I have a question about standardizing variables BEFORE running your Mplus analyses, such that the output would replicate STDYX output. I am interested in doing this to see if certain predictors are statistically stronger than others (by setting them to equivalence and seeing if model fit decreases), and want them to be standardized at the outset.

When you input the code, Mplus assumes that you are setting

**unstandardized**coefficients to equivalence. However, can you "trick" Mplus and set standardized coefficients to equivalence by standardizing the variables beforehand?My sense is that you can do this with observed variables without issues--the "unstandardized" output should almost be identical to STDYX.

However, how can you do this same trick with latent variables? I set the latent variable variances to 1, similar to standardized variables. However, when I looked this up online to see if it would be the same as STDYX, Bengt Muthen replied to someone else:

**I think you are asking if your raw estimates when (1) fixing factor variance to one and having all loadings free should be the same as the STDYX estimates when (2) using the Mplus default. If that's the question,**__the answer is no because in (1) your observed indicators are not standardized.__I then tried standardizing the indicators via Mplus code, but the "unstandardized" output did not replicate the STDYX output exactly.

__Any ideas about how to make BOTH observed and latent variables "standardized" in the "unstandardized" output?__Any help would be great!

**JamieAmemiya**- Moderator
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## Re: Other Longitudinal Methods (Cross-Lag, Latent Difference Score models)

Hi Jamie,

Because this is posted in the longitudinal section, I have to wonder, are you trying to do this in a longitudinal framework? If so, you may want to give some thought to whether you really do want to fully standardize all variables. That is, if you standardize at each time-point, you throw away information about the means or any change. If you are interested in studying non-regression paths (i.e., correlations or covariances) among latent variables, you might might want to consider the phantom variable approach discussed in Little (2013).

The issue that Bengt raises is that if you fix a factor variance to 1, you effectively standardize it. If you just want to have standardized predictor variables, you may do this as well. However, if you want to predict the factor indicators at the same time, then you will run in to trouble there.

Here is another thought. I think the issue you are trying to address doesn't require standardizing per se, but rather getting variables on the same scale of measurement, such that a 1 unit change on each means the same thing. One of the challenges with standardizing, is that it not only rescales the variables, but then equates the variances of variables that may naturally have different meaningful variances. So, what you could do is place variables on the same scale (e.g., make it so everything ranges from 1-10), but not standardize the variances. Then the coefficients would be meaningful to compare, without imposing problematic assumptions like the variances of all variables are the same.

Just some thoughts.

a

Because this is posted in the longitudinal section, I have to wonder, are you trying to do this in a longitudinal framework? If so, you may want to give some thought to whether you really do want to fully standardize all variables. That is, if you standardize at each time-point, you throw away information about the means or any change. If you are interested in studying non-regression paths (i.e., correlations or covariances) among latent variables, you might might want to consider the phantom variable approach discussed in Little (2013).

The issue that Bengt raises is that if you fix a factor variance to 1, you effectively standardize it. If you just want to have standardized predictor variables, you may do this as well. However, if you want to predict the factor indicators at the same time, then you will run in to trouble there.

Here is another thought. I think the issue you are trying to address doesn't require standardizing per se, but rather getting variables on the same scale of measurement, such that a 1 unit change on each means the same thing. One of the challenges with standardizing, is that it not only rescales the variables, but then equates the variances of variables that may naturally have different meaningful variances. So, what you could do is place variables on the same scale (e.g., make it so everything ranges from 1-10), but not standardize the variances. Then the coefficients would be meaningful to compare, without imposing problematic assumptions like the variances of all variables are the same.

Just some thoughts.

a

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