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Latent variable regression in lme4 as in HLM

5 messages · Uanhoro, James, Ben Bolker, Simon Harmel

Original
Simon Harmel
# 
Dear All,

I know that in the HLM software, it is possible to use "intercept" (e.g.,
initial place of students at year "0") as the *predictor *of "slope" (e.g.,
fixed rate of change in years) under the *Latent Variable Regression *tab.

I was wondering if this is also possible in "lme4" or any other
mixed-modeling packages in R?  *Thanks, Simon*

*## Here is an example dataset for demonstration:*
library(lme4)
dat <- read.csv('https://raw.githubusercontent.com/hkil/m/master/z.csv')
m1 <- lmer(y ~ year + (1|stid), data = dat)      #### 'stid' = student id
Uanhoro, James
# 
Hello Simon,

I'm not sure what HLM does. However: if your question is about using
the random intercepts (individuals' starting points) to predict the
random slopes (their linear growth rate), then the model you need is:

summary(m2 <- lmer(y ~ year + (1 + year | stid), dat))

whcih returns the random intercept and a random slope on time.

The correlation between both random effects is the regression
coefficient from regressing the slope on the intercept (or vice-versa)
when both variables are standardized.

More generally, you can always obtain regression coefficients from a
correlation/covariance matrix of random effects. With a two-by-two
correlation matrix, the single correlation is the coefficient (in both
directions). In a larger matrix of random effects, you can use the
solve() function in R to obtain coefficients from the matrix. See here:
https://stackoverflow.com/questions/40762865/how-do-i-get-regression-
coefficients-from-a-variance-covariance-matrix-in-r

I tried your exact example, and m2 above will not fit because some of
your participants have under 2 time points while the maximum number of
time points is 3, resulting in a situation where the software is
attempting to compute more random effect values than there are rows in
the data - the software complains. Also, it is a good idea to rescale
that y variable prior to data analysis. I was able to get the model to
run by limiting the data to cases with more than 1 recorded time point:

summary(m3 <- lmer(y.s ~ year + (1 + year | stid), data = t.dat, subset
= n > 1))

I arrived at a correlation/coefficient of -0.06.

Hope this helps, -James.

Sent from Outlook Mobile

From: R-sig-mixed-models <r-sig-mixed-models-bounces at r-project.org> on
behalf of Simon Harmel <sim.harmel at gmail.com>
Sent: Tuesday, May 26, 2020, 18:27
To: r-sig-mixed-models
Subject: [R-sig-ME] Latent variable regression in lme4 as in HLM

Dear All,

I know that in the HLM software, it is possible to use "intercept"
(e.g.,
initial place of students at year "0") as the *predictor *of "slope"
(e.g.,
fixed rate of change in years) under the *Latent Variable Regression
*tab.

I was wondering if this is also possible in "lme4" or any other
mixed-modeling packages in R?  *Thanks, Simon*

*## Here is an example dataset for demonstration:*
library(lme4)
dat <- read.csv('
https://urldefense.com/v3/__https://raw.githubusercontent.com/hkil/m/master/z.csv__;!!KGKeukY!gjIgidLro6PaJJUHZOY1gk9IW8FfrzGWzo9IEaCRgFwkorvpE1tkLXqn3ujcsmy6OvxsB2xlUIM$
 ')
m1 <- lmer(y ~ year + (1|stid), data = dat)      #### 'stid' = student
id


_______________________________________________
R-sig-mixed-models at r-project.org mailing list

https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!KGKeukY!gjIgidLro6PaJJUHZOY1gk9IW8FfrzGWzo9IEaCRgFwkorvpE1tkLXqn3ujcsmy6Ovxs517Hn00$
Ben Bolker
# 
For what it's worth, *if* you're sufficiently sure that your model
is identifiable, you can override the checks that test the relative
numbers of observations/levels/etc.; see the "check.*" options in
?lme4::lmerControl, and set the relevant ones to "ignore"

On Tue, May 26, 2020 at 7:12 PM Uanhoro, James
<uanhoro.1 at buckeyemail.osu.edu> wrote:
Simon Harmel
# 
Dear James,

Thanks for your response. I should research this a bit more. I have the
feeling that HLM software under the *Latent Variable Regression *tab might
be doing something different. But I highly appreciate you insightful
response.

Dear Ben,  lmerControl(check.nobs.vs.nRE="ignore") didn't work.

library(lme4)
dat <- read.csv('https://raw.githubusercontent.com/hkil/m/master/z.csv')
m1 <- lmer(y~ year + (year|stid), data = dat,
           control=lmerControl(check.nobs.vs.nRE="ignore"))
On Tue, May 26, 2020 at 7:38 PM Ben Bolker <bbolker at gmail.com> wrote:

            

      
      
      
    

        

      
      
    

            
        

      
      
    

            

      
      
      
    

        

  
  


  


      

    

    

      
      

        


  

        

      Ben Bolker
    

    

      
      #
    

  


  

      
On 5/26/20 10:12 PM, Simon Harmel wrote:

            

      
      
      
    

        
?? Really?? (Whenever you say "didn't work" you should give more 
detail; as I show below, it worked on my platform.? That it didn't work 
for you could mean a lot of different things [e.g. it really didn't work 
on your computer due to differences in lme4 version or OS or R version 
or ... ; you misinterpreted the results; ... Knowing what didn't work 
gives us a big head-start in helping you resolve the problem ...)

 ?? I think it did what it was intended to do, which is bypass the check 
of numbers of obs vs number of random effect levels.

 ? I get:

 ?? Warning message:
In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,? :
 ? Model failed to converge with max|grad| = 0.0028078 (tol = 0.002, 
component 1)

 ? However, the results look sensible.? Further exploration:

 ?? aa <- allFit(m1)

 > aa
original model:
y ~ year + (year | stid)
data:? dat
optimizers (7): bobyqa, Nelder_Mead, nlminbwrap, nmkbw, 
optimx.L-BFGS-B,nloptwrap.NLOPT_LN_N...
differences in negative log-likelihoods:
max= 4.25e-06 ; std dev= 1.58e-06


summary(aa)

 ? Differences among parameter estimates, log-likelihoods, etc. are all 
very small, so the convergence warning is a false positive.

 ? cheers

 ??? Ben Bolker