plm or lme4 for Random and Fixed Effects model on Panel Data

Question

Can I specify a Random and a Fixed Effects model on Panel Data using lme4?

I am redoing Example 14.4 from Wooldridge (2013, p. 494-5) in r. Thanks to this site and this blog post I've manged to do it in the plm package, but I'm curious if I can do the same in the lme4 package?

Here's what I've done in the plm package. Would be grateful for any pointers as to how I can do the same using lme4. First, packages needed and loading of data,

# install.packages(c("wooldridge", "plm", "stargazer"), dependencies = TRUE)
library(wooldridge) 
data(wagepan)

Second, I estimate the three models estimated in Example 14.4 (Wooldridge 2013) using the plm package,

library(plm) 
Pooled.ols <- plm(lwage ~ educ + black + hisp + exper+I(exper^2)+ married + union +
                  factor(year), data = wagepan, index=c("nr","year") , model="pooling")

random.effects <- plm(lwage ~ educ + black + hisp + exper + I(exper^2) + married + union +
                      factor(year), data = wagepan, index = c("nr","year") , model = "random") 

fixed.effects <- plm(lwage ~ I(exper^2) + married + union + factor(year), 
                     data = wagepan, index = c("nr","year"), model="within")

Third, I output the resultants using stargazer to emulate Table 14.2 in Wooldridge (2013),

stargazer::stargazer(Pooled.ols,random.effects,fixed.effects, type="text",
           column.labels=c("OLS (pooled)","Random Effects","Fixed Effects"), 
          dep.var.labels = c("log(wage)"), keep.stat=c("n"),
          keep=c("edu","bla","his","exp","marr","union"), align = TRUE, digits = 4)
#> ======================================================
#>                         Dependent variable:           
#>              -----------------------------------------
#>                              log(wage)                
#>              OLS (pooled) Random Effects Fixed Effects
#>                  (1)           (2)            (3)     
#> ------------------------------------------------------
#> educ          0.0913***     0.0919***                 
#>                (0.0052)      (0.0107)                 
#>                                                       
#> black         -0.1392***    -0.1394***                
#>                (0.0236)      (0.0477)                 
#>                                                       
#> hisp            0.0160        0.0217                  
#>                (0.0208)      (0.0426)                 
#>                                                       
#> exper         0.0672***     0.1058***                 
#>                (0.0137)      (0.0154)                 
#>                                                       
#> I(exper2)     -0.0024***    -0.0047***    -0.0052***  
#>                (0.0008)      (0.0007)      (0.0007)   
#>                                                       
#> married       0.1083***     0.0640***      0.0467**   
#>                (0.0157)      (0.0168)      (0.0183)   
#>                                                       
#> union         0.1825***     0.1061***      0.0800***  
#>                (0.0172)      (0.0179)      (0.0193)   
#>                                                       
#> ------------------------------------------------------
#> Observations    4,360         4,360          4,360    
#> ======================================================
#> Note:                      *p<0.1; **p<0.05; ***p<0.01

is there an equally simple way to do this in lme4? Should I stick to plm? Why/Why not?

@Jaap, thank you for your comment. I see it as a mainly programmers question, and not really a statistical/Cross Validated question. But I'm happy to move it if you think if belongs in CV. — Eric Fail
Please note that lme4 is about the maximum likely framework, so it won't be the "same": plm's vignette ch. 7 has some comparison to pkg nlme which is similar to lme4 and you should be able to take it from there. — Helix123
@Helix123, thank you for your comment. I will look into that. — Eric Fail

Gilles Gilles · Accepted Answer · 2018-03-08T08:49:59

Excepted for the difference in estimation method it seems indeed to be mainly a question of vocabulary and syntax

# install.packages(c("wooldridge", "plm", "stargazer", "lme4"), dependencies = TRUE)
library(wooldridge) 
library(plm) 
#> Le chargement a nécessité le package : Formula
library(lme4)
#> Le chargement a nécessité le package : Matrix
data(wagepan)

Your first example is a simple linear model ignoring the groups nr.
You can't do that with lme4 because there is no "random effect" (in the lme4 sense).
This is what Gelman & Hill call a complete pooling approach.

Pooled.ols <- plm(lwage ~ educ + black + hisp + exper+I(exper^2)+ married + 
                      union + factor(year), data = wagepan, 
                  index=c("nr","year"), model="pooling")

Pooled.ols.lm <- lm(lwage ~ educ + black + hisp + exper+I(exper^2)+ married + union +
                      factor(year), data = wagepan)

Your second example seems to be equivalent to a random intercept mixed model with nr as random effect (but the slopes of all predictors are fixed).
This is what Gelman & Hill call a partial pooling approach.

random.effects <- plm(lwage ~ educ + black + hisp + exper + I(exper^2) + married + 
                          union + factor(year), data = wagepan, 
                      index = c("nr","year") , model = "random") 

random.effects.lme4 <- lmer(lwage ~ educ + black + hisp + exper + I(exper^2) + married + 
                                union + factor(year) + (1|nr), data = wagepan)

Your third example seems to correspond to a case were nr is a fixed effect and you compute a different nr intercept for each group.
Again : you can't do that with lme4 because there is no "random effect" (in the lme4 sense).
This is what Gelman & Hill call a "no pooling" approach.

fixed.effects <- plm(lwage ~ I(exper^2) + married + union + factor(year), 
                     data = wagepan, index = c("nr","year"), model="within")

wagepan$nr <- factor(wagepan$nr)
fixed.effects.lm <- lm(lwage ~  I(exper^2) + married + union + factor(year) + nr, 
                     data = wagepan)

Compare the results :

stargazer::stargazer(Pooled.ols, Pooled.ols.lm, 
                     random.effects, random.effects.lme4 , 
                     fixed.effects, fixed.effects.lm,
                     type="text",
                     column.labels=c("OLS (pooled)", "lm no pool.",
                                     "Random Effects", "lme4 partial pool.", 
                                     "Fixed Effects", "lm compl. pool."), 
                     dep.var.labels = c("log(wage)"), 
                     keep.stat=c("n"),
                     keep=c("edu","bla","his","exp","marr","union"), 
                     align = TRUE, digits = 4)
#> 
#> =====================================================================================================
#>                                                Dependent variable:                                   
#>              ----------------------------------------------------------------------------------------
#>                                                     log(wage)                                        
#>                 panel         OLS         panel            linear           panel           OLS      
#>                 linear                    linear       mixed-effects       linear                    
#>              OLS (pooled) lm no pool. Random Effects lme4 partial pool. Fixed Effects lm compl. pool.
#>                  (1)          (2)          (3)              (4)              (5)            (6)      
#> -----------------------------------------------------------------------------------------------------
#> educ          0.0913***    0.0913***    0.0919***        0.0919***                                   
#>                (0.0052)    (0.0052)      (0.0107)         (0.0108)                                   
#>                                                                                                      
#> black         -0.1392***  -0.1392***    -0.1394***       -0.1394***                                  
#>                (0.0236)    (0.0236)      (0.0477)         (0.0485)                                   
#>                                                                                                      
#> hisp            0.0160      0.0160        0.0217           0.0218                                    
#>                (0.0208)    (0.0208)      (0.0426)         (0.0433)                                   
#>                                                                                                      
#> exper         0.0672***    0.0672***    0.1058***        0.1060***                                   
#>                (0.0137)    (0.0137)      (0.0154)         (0.0155)                                   
#>                                                                                                      
#> I(exper2)     -0.0024***  -0.0024***    -0.0047***       -0.0047***      -0.0052***     -0.0052***   
#>                (0.0008)    (0.0008)      (0.0007)         (0.0007)        (0.0007)       (0.0007)    
#>                                                                                                      
#> married       0.1083***    0.1083***    0.0640***        0.0635***        0.0467**       0.0467**    
#>                (0.0157)    (0.0157)      (0.0168)         (0.0168)        (0.0183)       (0.0183)    
#>                                                                                                      
#> union         0.1825***    0.1825***    0.1061***        0.1053***        0.0800***      0.0800***   
#>                (0.0172)    (0.0172)      (0.0179)         (0.0179)        (0.0193)       (0.0193)    
#>                                                                                                      
#> -----------------------------------------------------------------------------------------------------
#> Observations    4,360        4,360        4,360            4,360            4,360          4,360     
#> =====================================================================================================
#> Note:                                                                     *p<0.1; **p<0.05; ***p<0.01

Gelman A, Hill J (2007) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press (a very very good book !)

Created on 2018-03-08 by the reprex package (v0.2.0).

plm or lme4 for Random and Fixed Effects model on Panel Data

1 Answers