Random effect variance differs between glmer() and lmer() function

I'm studying the difference of feed intake between more than 150 horses. From each horse we have their feed intake at different week points.

My data is not normal-distributed. Therefore, in order to construct a linear mixed model (fixed effect: weeks and random effect: horse) I need to go through glmer() instead of lmer() in package lme4().

In glmer, the lower AIC obtained is through Gamma distribution.

Nevertheless I cannot understand that in glmer()model the variance of my random effect (horse) is only 6%(0.0646), in contrast if we considering normality and performing lmer(), then this 6% increase up to 33% (0.33159).

I'm more agree with the variance of my random effect stated by lmer() model instead of glmer() because a Horse will be an important variable to explain the model.

But, how I should interpret my results in order to discuss it properly?


# ASSUMING NORMALITY OF MY RESPONSE VARIABLE (Feed_kg_DM_day)

m_avg=lmer (Feed_kg_DM_day ~ factor(Week) + (1|Horse), data=dietdef)
summary(m_avg)

# Linear mixed model fit by REML ['lmerMod']
# Formula: Feed_kg_DM_day ~ factor(Week) + (1 | Horse)
# Data: dietdef
#
# REML criterion at convergence: 551.5
#
# Scaled residuals:
#   Min      1Q  Median      3Q     Max
# -8.6200 -0.1579 -0.0242  0.1094  7.6845
#
# Random effects:
#   Groups   Name        Variance Std.Dev.
# Horse    (Intercept) 0.33159  0.5758
# Residual             0.05074  0.2253
# Number of obs: 2909, groups:  Horse, 194
#
# Fixed effects:
#   Estimate Std. Error t value
# (Intercept)     3.162e+00  4.439e-02  71.222
# factor(Week)13 -4.479e-13  2.287e-02   0.000
# factor(Week)15 -6.610e-03  2.290e-02  -0.289
# factor(Week)17  2.000e-03  2.287e-02   0.087
# factor(Week)19  2.000e-03  2.287e-02   0.087
# factor(Week)2  -1.233e-02  2.287e-02  -0.539
# factor(Week)22  2.000e-03  2.287e-02   0.087
# factor(Week)24  2.000e-03  2.287e-02   0.087
# factor(Week)4  -1.233e-02  2.287e-02  -0.539
# factor(Week)43 -8.332e-02  2.287e-02  -3.643
# factor(Week)45  3.582e-02  2.287e-02   1.566
# factor(Week)47 -1.066e-03  2.287e-02  -0.047
# factor(Week)48 -1.852e-03  2.287e-02  -0.081
# factor(Week)7  -8.765e-03  2.287e-02  -0.383
# factor(Week)9  -5.115e-03  2.287e-02  -0.224

# ASSUMING NOT NORMALITY

summary(modelg2)

# Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
# Family: Gamma  ( identity )
# Formula: Feed_kg_DM_day ~ factor(Week) + (1 | Horse)
# Data: dietdef
#
# AIC      BIC   logLik deviance df.resid
# 92.9    194.5    -29.4     58.9     2892
#
# Scaled residuals:
#   Min      1Q  Median      3Q     Max
# -6.7920 -0.1935 -0.0464  0.1683  6.1595
#
# Random effects:
#   Groups   Name        Variance Std.Dev.
# Horse    (Intercept) 0.064600 0.2542
# Residual             0.006972 0.0835
# Number of obs: 2909, groups:  Horse, 194
#
# Fixed effects:
#   Estimate Std. Error t value Pr(>|z|)
# (Intercept)     3.304e+00  6.262e-02  52.753  < 2e-16 ***
#   factor(Week)13 -6.481e-06  2.196e-02   0.000  0.99976
# factor(Week)15 -8.264e-03  2.197e-02  -0.376  0.70678
# factor(Week)17 -5.430e-03  2.195e-02  -0.247  0.80466
# factor(Week)19 -5.430e-03  2.195e-02  -0.247  0.80465
# factor(Week)2  -1.186e-02  2.191e-02  -0.541  0.58832
# factor(Week)22 -5.429e-03  2.195e-02  -0.247  0.80469
# factor(Week)24 -5.434e-03  2.195e-02  -0.248  0.80451
# factor(Week)4  -1.186e-02  2.191e-02  -0.541  0.58846
# factor(Week)43 -3.059e-02  2.181e-02  -1.403  0.16067
# factor(Week)45  7.184e-02  2.222e-02   3.233  0.00123 **
#   factor(Week)47  3.180e-02  2.206e-02   1.442  0.14942
# factor(Week)48  4.943e-02  2.206e-02   2.241  0.02505 *
#   factor(Week)7  -9.628e-03  2.192e-02  -0.439  0.66052
# factor(Week)9  -7.088e-03  2.193e-02  -0.323  0.74657
# ---
#   Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
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• Not sure why people are voting to close this since there is a statistical issue here (I think, or at least an issue with the OP understanding of the random effects) which I have tried to answer. – mdewey Apr 26 '19 at 11:47