question about random coefficients model (RCM) - R-SIG-mixed-models

Thu, May 5, 2011 9:26 AM #

Dear Jose,

Did you ever figure out how to replicate Western's (1998) model using lme4?

I've figured out how to replicate precisely the "Interactions Model" in his Table 2, but not the "Hierarchical Model"--see code below. I'm not sure if the issue is the estimation technique (REML rather than a Gibbs sampler), or if I've just not understood the model. I've also tried using MCMCglmm but am not having much more luck with that--other than the intercept, all fixed effects span 0, unlike in the results that Western reports.

I'd be interested to know if you found a way to replicate Western's results more precisely.

Cheers,
Malcolm


library(pcse) # includes the relevant dataset
data(agl)
agl2 <- agl[agl$year!=1970,]
agl2$lgrowth <- as.vector(unlist(by(agl, agl$country, function(x) x$growth[-15]))) # create lagged y variable
for (i in c(5:8, 11)) { agl2[,i] <- as.vector(unlist(by(agl2, agl2$country, function(x) scale(x[,i], scale=F)))) } # to center the time-series predictors within countries
w98.eq11 <- lm(growth ~ lgrowth*central + opengdp*central + openex*central + openimp*central + leftc*central, data=agl2) # matches the "Interactions Model" in Table 2
library(lme4)
w98.eq13 <- lmer(growth ~ lgrowth*central + opengdp*central + openex*central + openimp*central + leftc*central + (lgrowth + opengdp + openex + openimp + leftc | country), data=agl2)
data.frame(round(fixef(w98.eq13), 3), round(coef(w98.eq11), 3)); ranef(w98.eq13)
library(MCMCglmm)
prior <- list(R = list(V = 1, nu = 0), G = list(G1 = list(V = diag(6), nu = 1)))
w98.eq13.MCMC <- MCMCglmm(growth ~ lgrowth*central + opengdp*central + openex*central + openimp*central + leftc*central, random=~us(1 + lgrowth + opengdp + openex + openimp + leftc):country, data=agl2, prior=prior)

Message: 5
Date: 30-Jul-2010 16:48:33 EDT
From: JOSE A ALEMAN <aleman at fordham.edu>
To: Andrew Dolman <andydolman at gmail.com>
Cc: dmbates at gmail.com, r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] question about random coefficients model (RCM)
Message-ID: <OF4E9738AC.B8F4A4AE-ON85257770.00710104 at fordham.edu>
Content-Type: text/plain; charset=ISO-8859-1

Hi Andy,

You're right, ranef() does actually work. Actually, data.neocorporatism is
pretty much a time-invariant institutional variable. What I want is to
estimate a random intercepts random slopes model where the effects of other
time varying variables enter the model through the institutional variable
"data.neocorporatism". The effects for neocorporatism, in other words,
should be different depending on the country, that is, there shouldn't be a
single coefficient for this variable but 18 different coefficients for the
18 different countries. If that's the case, then "data.neocorporatism"
should not be in the fixed effects equation.

I indeed tried the model having removed this variable, but the result after
typing coef() was the same. Actually, ranef() gave me what I believe are
the random intercepts for each country, but I still need to figure out a
way to get the coefficients.

I'm probably doing something wrong, but I am basically trying to fit a
model similar to Western's (1998) described in my original message below.

Thank you,

Jose

            Andrew Dolman                                                 
            <andydolman at gmail                                             
            .com>                                                      To 
                                      JOSE A ALEMAN <aleman at fordham.edu>  
            07/30/2010 03:45                                           cc 
            PM                        Douglas Bates                       
                                      <bates at stat.wisc.edu>,              
                                      dmbates at gmail.com,                  
                                      r-sig-mixed-models at r-project.org    
                                                                  Subject 
                                      Re: [R-sig-ME] question about       
                                      random coefficients model (RCM)     

Hi Jose

data.nation is not present in the the fixed effects specification of
your model, so coef() won't work, but ranef() should. Your model
assumes that there is no overall relationship between data.gini_net
and data.nation and yet allows for a relationship within the
sub-groups defined by data.neocorporatism_std, with a slope that
varies randomly between groups but is zero overall. That's probably
not what you want.

I also notice that data.neocorporatism seems to have been standardised
somehow, which would be odd for a categorical variable used to group
things.

andydolman at gmail.com

On 30 July 2010 18:52, JOSE A ALEMAN <aleman at fordham.edu> wrote:

The model I'm using is of the form:

RCM <- lmer (data.gini_net ~ data.neocorporatism_std +
data.firm_level_coop_std + data.cog + data.gov_employ_std +
? ? ?data.netden_std + data.trade_openness_std +
data.capital_liberalization_std + data.lagged_unemploy_std +
? ? ?data.deindustrialization_std + data.pop_over_65_percent_std +
(data.nation|data.neocorporatism_std), data=new.data)

but when I try to use the extractor coef(), I get the following error
message:

coef(RCM)

Error in coef(RCM) : unable to align random and fixed effects




? ? ? ? ? ? Douglas Bates
? ? ? ? ? ? <bates at stat.wisc.
? ? ? ? ? ? edu> ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? To
? ? ? ? ? ? Sent by: ? ? ? ? ? ? ? ? ?JOSE A ALEMAN <aleman at fordham.edu>
? ? ? ? ? ? dmbates at gmail.com ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?cc
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? r-sig-mixed-models at r-project.org
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Subject
? ? ? ? ? ? 07/17/2010 11:30 ? ? ? ? ?Re: [R-sig-ME] question about
? ? ? ? ? ? AM ? ? ? ? ? ? ? ? ? ? ? ?random coefficients model (RCM)


On Sat, Jul 17, 2010 at 9:52 AM, JOSE A ALEMAN <aleman at fordham.edu>

wrote:

Dear list users,

I have a question about how to estimate the RCM described by Western

(1998)

in his article "Causal Heterogeneity in Comparative Research: A Bayesian
Hierarchical Modeling Approach". While I know how to estimate this model

in

R via restricted maximum likelihood, I am at a loss as to how to

interpret

the results. The random coefficients are supposed to be different for

each

country, yet R provides ?a standard regression-like output with a single
coefficient for the variable with the random slope. How would I go about
extracting the country specific information?

Can you be more specific about how you fit the model? ?Just saying "in
R" is too general.

If you fit the model with lmer from the lme4 package then you may want
to look at the output from the ranef() and coef() extractors.