Cross-lagged panel model with ordinal data in Lavaan

[Hannah Pickard]

Hi everyone, 

I am conducting a longitudinal investigation exploring the relationship between autistic traits (AT/AutTrait) and social anxiety (SA/SocFears) symptoms in children at 7, 10 and 13 years old. The AT scale has 12 items (1-3 scale) and the SA scale has 6 items (1-4 scale), so I will be treating both of these as ordinal variables. I have created a latent variable for each questionnaire at the 3 separate time points that I will be using within a crossed lagged panel model. 

This is an example of my model:

I have a number of issues

1) I would like to know whether I am adequately controlling for the autoregressive pathways (a, b, c and d) when exploring my cross lagged paths (e, f, g and h)? (see code in red)

###################### Cross-lagged panel model ##########################

clpm2 <- '

#latent variables age 7

SF7 =~ Sfears7_Q1 + Sfears7_Q2 + Sfears7_Q3 + Sfears7_Q4 + Sfears7_Q5 + Sfears7_Q6

AT7 =~ SC7_Q1 + SC7_Q2 + SC7_Q3 + SC7_Q4 + SC7_Q5 + SC7_Q6 + SC7_Q7 + SC7_Q8 + SC7_Q9 + SC7_Q10 + SC7_Q11 + SC7_Q12

#latent variable age 10

SF10 =~ Sfears10_Q1 + Sfears10_Q2 + Sfears10_Q3 + Sfears10_Q4 + Sfears10_Q5 + Sfears10_Q6

AT10 =~ SC10_Q1 + SC10_Q2 + SC10_Q3 + SC10_Q4 + SC10_Q5 + SC10_Q6 + SC10_Q7 + SC10_Q8 + SC10_Q9 + SC10_Q10 + SC10_Q11 + SC10_Q12

#latent variable age 13

SF13 =~ Sfears13_Q1 + Sfears13_Q2 + Sfears13_Q3 + Sfears13_Q4 + Sfears13_Q5 + Sfears13_Q6

AT13 =~ SC13_Q1 + SC13_Q2 + SC13_Q3 + SC13_Q4 + SC13_Q5 + SC13_Q6 + SC13_Q7 + SC13_Q8 + SC13_Q9 + SC13_Q10 + SC13_Q11 + SC13_Q12

#covariances

AT7 ~~ SF7

AT10 ~~ SF10

AT13 ~~ SF13

#autoregressive and cross-lagged paths

SF10 ~ AT7 + SF7

AT10 ~ SF7 + AT7

SF13 ~ AT10 + SF10

AT13 ~ SF10 + AT10

'

2) What is the best way to deal with missing data across time points in my sample? Some individuals have data at time point one (T1: age 7) and not at T2 (age 10) or T3 (age 13), whereas others have data at T2 and T3 but not at T1. I have come across the full information maximum likelihood (FIML) method for missing data, however, this is not an option using the sem() function with ordinal data in Lavaan. Instead they suggest using the pairwise maximum likelihood (PML) method, however, I am not 100% sure how this works. Any advice on this would be great!!! 

I have been able to find only limited information regarding cross-lagged panel models in Lavaan, so any help would be really appreciated.

Thanks,

Hannah

[Terrence Jorgensen]

1) I would like to know whether I am adequately controlling for the autoregressive pathways (a, b, c and d) when exploring my cross lagged paths (e, f, g and h)? (see code in red)

Yes, your syntax matches your path diagram, which assumes a simplex (AR1) structure.  If the model doesn't fit well, you can also test an AR2 structure (i.e., whether you need to regress T3 on both T2 and T1) by adding those regression paths.

they suggest using the pairwise maximum likelihood (PML) method, however, I am not 100% sure how this works

Set the option missing = "pairwise", and lavaan will estimate polychoric correlations using pairwise MLE.  Make sure to declare your indicators as ordinal if they are not already of class "ordered" in your data.frame, and lavaan will use the appropriate DWLS estimator to fit your model to those polychoric correlations. 

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

[Hannah Pickard]

Hi Terrence,

Thank you very much for your response. That has cleared a lot of things up for me!

I just have a one more question regarding my output.

Here is my model:

and here is the output I get when I run my CLPM:

1) When reporting my results do I focus on the DWLS or robust column, as I am not 100% sure what the robust statistics are referring to in this instance? If you could tell me more about the robust statistics that would be great.

Thank you very much for all of your help!

Hannah

[Terrence Jorgensen]

When reporting my results do I focus on the DWLS or robust column, as I am not 100% sure what the robust statistics are referring to in this instance?

Pay attention to the Robust column.  Unadjusted test statistics typically have inflated Type I error rates.

If you could tell me more about the robust statistics that would be great.

Here is a link to a paper explaining robust corrections:

http://dx.doi.org/10.1080/10705511.2013.824793