Growth curve model

[Marcos Angelini]

Dear community,

I have a basic question about growth curve models.

I want to analyse the factors that affect crop production. For this, lets assume that I have the crop production per administrative unit (100 counties) per year (four years). Among the variables that affect crop productions, some vary among counties but not in time, such as surface of the county; others varies among counties and in times, such as crop surface; and I have another variable type that varies in time but not among counties, such as crop price.

My question is, how do I treat this last variable?

Lets assume that

• CP0 to CP3 is crop production (in tons) per county for the first to the fourth year;
  
• S is county surface (in hectares);
  
• C0 to C3 is crop surface (in hectares) per county for the first to the fourth year; and
  
• D0 to D3 is the crop price (in USD/tons of crop) for the first to the fourth year.

Base on the lavaan tutorial, I set the model in this way

model <- '
  # intercept and slope with fixed coefficients
    i =~ 1*CP0 + 1*CP1 + 1*CP2 + 1*CP3
    s =~ 0*CP0 + 1*CP1 + 2*CP2 + 3*CP3
  # regressions
    i ~ S
    s ~ S
  # time-varying covariates
    CP0 ~ C0 + D0
    CP1 ~ C1 + D1
    CP2 ~ C2 + D2
    CP3 ~ C3 + D3
'

D will be constant for all counties (it means that in the data frame, D0 will be the same for all counties). Is that correct?

[Terrence Jorgensen]

how do I treat this last variable?

If your data are nested within counties, you need a multilevel model

http://lavaan.ugent.be/tutorial/multilevel.html

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

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

http://www.uva.nl/profile/t.d.jorgensen

[Marcos Angelini]

Dear Terrence,

Thanks for your reply.

The data would is clustered by counties. That is right. But, how do you suggest I handle the years?

Thanks in advance,

Marcos

[Terrence Jorgensen]

But, how do you suggest I handle the years?

It looks like you are already handling years.  The data are in wide format, so they are not "multilevel" with respect to time.  Rather, they are multivariate.  These are equivalent ways to handle longitudinal data (nesting of occasions within cases):

https://doi.org/10.3102/10769986028002135

https://doi.org/10.1207/s15327906mbr3804_5

You can even handle nesting of cases within clusters in a multivariate way, although it is quite clumsy and tedious.  This article provides a decent teaching example, showing how random effects and factor scores are really the same thing:

https://www.statmodel.com/download/mehtaneale.PDF

Anyway, you are in the lucky position of being able to fit a 2-level model to handle 3-level data because the nesting of occasions within cases is handled in a multivariate way.

[Marcos Angelini]

Thanks a lot Terrence! I will read these references.