Uneven Samples at each wave in non-experimental Random Intercept Cross-Lagged Panel Model

[Atanas Janackovski]

Hi, this is more a stats question than a lavaan question, but given I am using lavaan, thought I may as well ask it here… Apologies if this is not okay. Here goes…

I have data from people attending psychological therapy in a non-experimental setting. As this is a naturalistic setting, participants attend a different number of sessions. The sample size is N = 639, with mean number of session of 5.24 (SD = 2.16, range = 2–13).

I want to test a number of different variables, and have included the total number of sessions attended as a covariate in the analysis (for the random intercept at least). I am using the R package lavaan, using "full information maximum likelihood" to estimate the missing data. So, for someone that has been discharged after 2 sessions, lavaan will handle the "missing" data.

My question is, can I actually use this type of analysis with this data set? Are there any assumptions I am violating by specifying the model this way?

I have searched the internet as well as looked for primary sources, however I cannot seem to find anything to help me. Please let me know if you need more information about my questions.

Thanks in advance.

[Pat Malone]

Atanas,

It would help to know more about your model (and research question).

If the participants have been discharged, there is almost certainly a reason that is not captured in the number of sessions. So if sessions are not interchangeable, data are missing not at random, meaning FIML cannot fully compensate, unless you have a lot more information in the model (perhaps from the final session?) that would contribute to knowing why the data are missing.

If sessions are interchangeable, you're probably ok with a multilevel model with sessions nested within participants, but that rules out longitudinal analyses.

Pat

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Patrick S. Malone, PhD

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[Pat Malone]

Ah, I just saw in the SEMNET version of this question that you are interested in longitudinal analysis. In that case, I suggest more careful attention to the MAR assumption beyond just number of sessions.

Pat

[Atanas Janackovski]

Thank you Pat.

So, the research question is related to testing the Interpersonal Psychological Theory of Suicide (IPTS) in a non-experimental clinical sample. See picture of purported path model below. The theory states that four factors: perceived burdensomeness, thwarted belongingness, hopelessness and acquired capability are necessary and required to lead to suicide. It also states, that address thwarted belongingness or perceived burdensomeness will lead to reductions in suicidal desire. However, depression is also commonly associated with suicidality.

Most the research has been cross-sectional in nature, even the ones that include more than one time point (including some I have been involved in). The models that have tested this before are mediated regression that used change scores to predicted change in suicidality. However, the underlying assumption to this type of "outcome" research, is that indeed the factors posited by the IPTS do indeed lead to suicidality. But, as most research is cross-sectional in nature, it has not looked at time-to-time changes in these factors. One recent study has used the RI-CLPM to ask this question, using beginning, mid and end point data from an RCT clinical intervention (Abbott, et. al., 2021). They found that the theory doesn't hold, that is, that changes in the theoretical variables don't predict changes in suicidality.

Regarding missing data, data for some participants is MNAR, because they have completed therapy after 2, 3, … n, sessions. For others, they will continue beyond the 5 waves that I am wanting to test (but may have missing data between sessions 2–4 for other reasons, although there is not too much missing in this regard, apart from one questionnaire not being complete, for example). I have the total sessions each person attended over their episode of therapy and was entering this as covariate loading onto the random intercepts (as well as age, sex, and acquired capability as baseline [as it was only measured once in the sample, and is theoretically consistent to only measure once as it is more 'trait' like]).

So, given this, is there any reason that I cannot use a RI-CLPM? If it is related to MNAR, what is the approach to this? Multiple imputation? Or is the design not able to be carried out at all?

I'm not sure if it is helpful or not, but have posted my code below just in case…

Thanks again for your help, and please let me know if you need any more information about by questions.

Interpersonal Psychological Theory of Suicide

 

(Van Orden, et. al, 2010)

Model specification

This was developed with the help of the Mulder and Hamaker (2020) article and example code.

riclpm_byc_si_cov <- '
  ## Create between components (random intercepts)
  RIpb  =~ 1*pb_1 + 1*pb_2 + 1*pb_3 + 1*pb_4 + 1*pb_5
  RItb  =~ 1*tb_1 + 1*tb_2 + 1*tb_3 + 1*tb_4 + 1*tb_5
  RIbhs =~ 1*bhs_1 + 1*bhs_2 + 1*bhs_3 + 1*bhs_4 + 1*bhs_5
  RIdep =~ 1*dep_1 + 1*dep_2 + 1*dep_3 + 1*dep_4 + 1*dep_5
  RIsi  =~ 1*si_1 + 1*si_2 + 1*si_3 + 1*si_4 + 1*si_5
  ## Create within-person centered variables
  wpb_1 =~ 1*pb_1
  wpb_2 =~ 1*pb_2
  wpb_3 =~ 1*pb_3
  wpb_4 =~ 1*pb_4
  wpb_5 =~ 1*pb_5
  ## ==
  wtb_1 =~ 1*tb_1
  wtb_2 =~ 1*tb_2
  wtb_3 =~ 1*tb_3
  wtb_4 =~ 1*tb_4
  wtb_5 =~ 1*tb_5
  ## ==
  wbhs_1 =~ 1*bhs_1
  wbhs_2 =~ 1*bhs_2
  wbhs_3 =~ 1*bhs_3
  wbhs_4 =~ 1*bhs_4
  wbhs_5 =~ 1*bhs_5
  ## ==
  wdep_1 =~ 1*dep_1
  wdep_2 =~ 1*dep_2
  wdep_3 =~ 1*dep_3
  wdep_4 =~ 1*dep_4
  wdep_5 =~ 1*dep_5
  ## ==
  wsi_1 =~ 1*si_1
  wsi_2 =~ 1*si_2
  wsi_3 =~ 1*si_3
  wsi_4 =~ 1*si_4
  wsi_5 =~ 1*si_5
  ##
  ## =======
  ## covariates
  ## =======
  ## Regression of random intercepts on covariates.
  ## -------
  RIpb + RItb + RIbhs + RIdep+ RIsi ~ ac_1 # Constrained over time.
  RIpb + RItb + RIbhs + RIdep+ RIsi ~ age
  RIpb + RItb + RIbhs + RIdep+ RIsi ~ sex_mf
  RIpb + RItb + RIbhs + RIdep+ RIsi ~ cov_sess
  ## =====
  ##
  ## Estimate the lagged effects between the within-person centered variables.
  wpb_2 + wtb_2 + wbhs_2 + wdep_2 + wsi_2 ~ wpb_1 + wtb_1 + wbhs_1 + wdep_1 + wsi_1
  wpb_3 + wtb_3 + wbhs_3 + wdep_3 + wsi_3 ~ wpb_2 + wtb_2 + wbhs_2 + wdep_2 + wsi_2
  wpb_4 + wtb_4 + wbhs_4 + wdep_4 + wsi_4 ~ wpb_3 + wtb_3 + wbhs_3 + wdep_3 + wsi_3
  wpb_5 + wtb_5 + wbhs_5 + wdep_5 + wsi_5 ~ wpb_4 + wtb_4 + wbhs_4 + wdep_4 + wsi_4
  ## ==
  ## Estimate the covariance between the within-person centered variables
  ## at the first wave.
  wpb_1  ~~ wtb_1 # Covariance
  wpb_1  ~~ wbhs_1
  wpb_1  ~~ wdep_1
  wpb_1  ~~ wsi_1
  wtb_1  ~~ wbhs_1
  wtb_1  ~~ wdep_1
  wtb_1  ~~ wsi_1
  wbhs_1 ~~ wsi_1
  wbhs_1 ~~ wdep_1
  wdep_1 ~~ wsi_1
  ## Estimate the covariances between the residuals of the within-person
  ## centered variables (the innovations).
  ## time_2
  wpb_2  ~~ wtb_2
  wpb_2  ~~ wbhs_2
  wpb_2  ~~ wdep_2
  wpb_2  ~~ wsi_2
  wtb_2  ~~ wbhs_2
  wtb_2  ~~ wdep_2
  wtb_2  ~~ wsi_2
  wbhs_2 ~~ wsi_2
  wbhs_2 ~~ wdep_2
  wdep_2 ~~ wsi_2
  ## time_3
  wpb_3  ~~ wtb_3
  wpb_3  ~~ wbhs_3
  wpb_3  ~~ wdep_3
  wpb_3  ~~ wsi_3
  wtb_3  ~~ wbhs_3
  wtb_3  ~~ wdep_3
  wtb_3  ~~ wsi_3
  wbhs_3 ~~ wsi_3
  wbhs_3 ~~ wdep_3
  wdep_3 ~~ wsi_3
  ## time_4
  wpb_4  ~~ wtb_4
  wpb_4  ~~ wbhs_4
  wpb_4  ~~ wdep_4
  wpb_4  ~~ wsi_4
  wtb_4  ~~ wbhs_4
  wtb_4  ~~ wdep_4
  wtb_4  ~~ wsi_4
  wbhs_4 ~~ wsi_4
  wbhs_4 ~~ wdep_4
  wdep_4 ~~ wsi_4
  ## time_5
  wpb_5  ~~ wtb_5
  wpb_5  ~~ wbhs_5
  wpb_5  ~~ wdep_5
  wpb_5  ~~ wsi_5
  wtb_5  ~~ wbhs_5
  wtb_5  ~~ wdep_5
  wtb_5  ~~ wsi_5
  wbhs_5 ~~ wsi_5
  wbhs_5 ~~ wdep_5
  wdep_5 ~~ wsi_5
  ## Estimate the variance and covariance of the random intercepts.
  RIpb  ~~ RIpb
  RItb  ~~ RItb
  RIbhs ~~ RIbhs
  RIdep ~~ RIdep
  RIsi  ~~ RIsi
  ## ==
  RIpb  ~~ RItb
  RIpb  ~~ RIbhs
  RIpb  ~~ RIdep
  RIpb  ~~ RIsi
  RItb  ~~ RIbhs
  RItb  ~~ RIdep
  RItb  ~~ RIsi
  RIbhs ~~ RIsi
  RIbhs ~~ RIdep
  RIdep ~~ RIsi
  ## Estimate the (residual) variance of the within-person centered variables.
  wpb_1  ~~ wpb_1 # Variances
  wtb_1  ~~ wtb_1
  wbhs_1 ~~ wbhs_1
  wdep_1 ~~ wdep_1
  wsi_1  ~~ wsi_1
  ## time_2
  wpb_2  ~~ wpb_2 # Residual variances
  wtb_2  ~~ wtb_2
  wbhs_2 ~~ wbhs_2
  wdep_2 ~~ wdep_2
  wsi_2  ~~ wsi_2
  ## time_3
  wpb_3  ~~ wpb_3 # Residual variances
  wtb_3  ~~ wtb_3
  wbhs_3 ~~ wbhs_3
  wdep_3 ~~ wdep_3
  wsi_3  ~~ wsi_3
  ## time_4
  wpb_4  ~~ wpb_4 # Residual variances
  wtb_4  ~~ wtb_4
  wbhs_4 ~~ wbhs_4
  wdep_4 ~~ wdep_4
  wsi_4  ~~ wsi_4
  ## time_5
  wpb_5  ~~ wpb_5 # Residual variances
  wtb_5  ~~ wtb_5
  wbhs_5 ~~ wbhs_5
  wdep_5 ~~ wdep_5
  wsi_5  ~~ wsi_5
'

References

Abbott, C. H., Zisk, A., Herres, J., Diamond, G. S., Krauthamer Ewing, S., & Kobak, R. (2021). Exploring the relations between interpersonal risk and adolescent suicidality during treatment. Journal of Consulting and Clinical Psychology, 89(6), 528–536. doi: 10/gmkb5v

Mulder, J.D. & Hamaker, E.L. (2020). Three extensions of the Random Intercept Cross-Lagged Panel Model. Structural Equation Modeling: A Multidisciplinary Journal, DOI: 10.1080/10705511.2020.1784738

Van Orden, K. A., Witte, T. K., Cukrowicz, K. C., Braithwaite, S. R., Selby, E. A., & Joiner, T. E. (2010). The interpersonal theory of suicide. Psychological Review, 117(2), 575–600. https://doi.org/10/b44zs2

[Pat Malone]

Atanas,

The fact that you're using RI-CLPM isn't a problem. It just means that some of the simpler solutions to your missingness problem won't be helpful. I don't  have specific suggestions for techniques to model the non-random missing with your SEM, but you might try the work of Craig Enders or Karthika Mohan (e.g., https://ftp.cs.ucla.edu/pub/stat_ser/r448-reprint.pdf looks like it might be helpful, but I haven't read it closely).

Good luck!

P.S. I was Dorian Lamis's doctoral mentor :)

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[Atanas Janackovski]

Thank you Pat. I've been looking at some approaches using the mice package  under MNAR, but I will look into these too. 

I've started a sensitivity analysis by dropping the observations with missing data and the pattern of results so far is similar. 

I'm glad that an RI-CLPM will be usable because I think this approach suits the aims of the study. But is it still okay that I only stop at 5 waves, even for those have more sessions?

Thanks again. 

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[Pat Malone]

Unfortunately, that  sensitivity analysis will only distinguish between MCAR and MAR.

Your missingness model may need to include a censoring process, but if you're doing a full missingness strategy for MNAR, that shouldn't be much of an extra issue.

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[Atanas Janackovski]

Oh, thanks for the clarification. Can you recommend any resources for me to learn more about censoring processes in missingness models?

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[Pat Malone]

I would look at the general methods for MNAR. We're getting beyond my expertise.

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[Atanas Janackovski]

No worries. Thanks so much, your advice has been very helpful!

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