# [R-sig-ME] anova() and the difference between (x | y) and (1 | y:x) in lme4

Hans Ekbrand hans.ekbrand at gmail.com
Wed Jun 11 15:58:10 CEST 2014

```Dear list,

I have a question about the difference between

y ~ (1 | var2:var1) vs y ~ (var1 | var2).

In reality my model is more complex:

y ~ 1 + var1 + (1 | var2:var1) + var3+ .... + var9

vs

y ~ 1 + var1 + (var1 | var2) + var3+ .... + var9

Following the advice kindly given by Reinhold Kliegl way back ago
(https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q2/016545.html)
I have used the following specification with glmer() in lme4 (version 1.1-7):

fit.flat <- glmer(below.poverty.line ~ 1 + employment.type + (1 | country:employment.type) + gender + age + age.2 + n.adults.minus.n.children + n.children + education + household.type, family = binomial("logit"), data = my.df)

and

fit.hierarchical <- glmer(below.poverty.line ~ 1 + employment.type + (employment.type | country) + gender + age + age.2 + n.adults.minus.n.children + n.children + education + household.type, family = binomial("logit"), data = my.df)

Info on the data:

str(my.df)
'data.frame':	93178 obs. of  10 variables:
\$ below.poverty.line       : logi  FALSE FALSE FALSE FALSE FALSE FALSE ...
\$ employment.type          : Factor w/ 6 levels "Core labour force",..: 1 5 1 1 1 5 5 5 1 1 ...
\$ country                  : Factor w/ 22 levels "austria","belgium",..: 1 1 1 1 1 1 1 1 1 1 ...
\$ gender                   : Factor w/ 2 levels "female","male": 2 1 2 2 1 1 1 1 2 2 ...
\$ age                      : num  22 22 32 56 40 54 42 18 49 20 ...
\$ age.2                    : num  3.39e-02 3.39e-02 7.08e-03 2.43e-02 1.71e-05 ...
\$ n.adults.minus.n.children: num  3 3 1 5 2 2 3 5 5 5 ...
\$ n.children               : num  1 1 2 0 1 0 1 0 0 0 ...
\$ education                : Factor w/ 4 levels "primary","lower secondary",..: 2 2 4 2 3 4 2 2 2 3 ...
\$ household.type           : Factor w/ 4 levels "couple without children",..: 2 2 3 1 3 4 3 4 1 4 ...

If you want to replicate the analysis - or inspect the data - try this:

The total computation time for both models is about one hour on my computer.

My primary question is whether or not anova() is usable to choose between the two models?

Data: my.df
Models:
fit.flat: below.poverty.line ~ 1 + employment.type + (1 | country:employment.type) +
fit.flat:     gender + age + age.2 + n.adults.minus.n.children + n.children +
fit.flat:     education + household.type
fit.hierarchical: below.poverty.line ~ 1 + employment.type + (employment.type |
fit.hierarchical:     country) + gender + age + age.2 + n.adults.minus.n.children +
fit.hierarchical:     n.children + education + household.type
Df   AIC   BIC logLik deviance  Chisq Chi Df Pr(>Chisq)
fit.flat         18 38852 39022 -19408    38816
fit.hierarchical 38 38804 39163 -19364    38728 88.082     20  1.602e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

My second question is whether or not I should care about the warnings
I get (not entirely sure which one belongs to which model, but the
first one should be against fit.hierarchcial).

Warning in checkConv(attr(opt, "derivs"), opt\$par, ctrl = control\$checkConv,  :
Model failed to converge with max|grad| = 0.00636715 (tol = 0.001, component 30)
Warning in checkConv(attr(opt, "derivs"), opt\$par, ctrl = control\$checkConv,  :
Model is nearly unidentifiable: very large eigenvalue
- Rescale variables?
Warning in checkConv(attr(opt, "derivs"), opt\$par, ctrl = control\$checkConv,  :
Model is nearly unidentifiable: very large eigenvalue
- Rescale variables?;Model is nearly unidentifiable: large eigenvalue ratio
- Rescale variables?

summary(fit.flat)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: binomial  ( logit )
Formula: below.poverty.line ~ 1 + employment.type + (1 | country:employment.type) +
gender + age + age.2 + n.adults.minus.n.children + n.children +      education + household.type
Data: my.df

AIC      BIC   logLik deviance df.resid
38852.1  39022.1 -19408.1  38816.1    93160

Scaled residuals:
Min      1Q  Median      3Q     Max
-1.5785 -0.2741 -0.1841 -0.1240 14.1696

Random effects:
Groups                  Name        Variance Std.Dev.
country:employment.type (Intercept) 0.301    0.5486
Number of obs: 93178, groups:  country:employment.type, 132

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)                                         -2.821530   0.164883 -17.112  < 2e-16 ***
employment.typeCore self-employed                    1.779764   0.177173  10.045  < 2e-16 ***
employment.typeInto core labour force                0.873362   0.183095   4.770 1.84e-06 ***
employment.typeMarginalized peripheral labour force  1.791760   0.185840   9.641  < 2e-16 ***
employment.typePeripheral labour force               1.036154   0.175026   5.920 3.22e-09 ***
employment.typePeripheral self-employed              1.699013   0.180444   9.416  < 2e-16 ***
gendermale                                           0.152666   0.029487   5.177 2.25e-07 ***
age                                                 -0.008906   0.001537  -5.794 6.86e-09 ***
age.2                                               -3.647558   1.044310  -3.493 0.000478 ***
n.adults.minus.n.children                            0.034069   0.010769   3.164 0.001559 **
n.children                                           0.258188   0.028628   9.019  < 2e-16 ***
educationlower secondary                            -0.399377   0.051611  -7.738 1.01e-14 ***
educationupper secondary                            -0.902910   0.049323 -18.306  < 2e-16 ***
educationpost secondary                             -1.582793   0.056489 -28.019  < 2e-16 ***
household.typecouple with children                  -0.120115   0.058652  -2.048 0.040568 *
household.typesingle adult with children             0.514623   0.069323   7.424 1.14e-13 ***
household.typesingle adult without children          0.195389   0.041295   4.732 2.23e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

summary(fit.hierarchical)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: binomial  ( logit )
Formula: below.poverty.line ~ 1 + employment.type + (employment.type |
country) + gender + age + age.2 + n.adults.minus.n.children +      n.children + education + household.type
Data: my.df

AIC      BIC   logLik deviance df.resid
38804.0  39162.8 -19364.0  38728.0    93140

Scaled residuals:
Min      1Q  Median      3Q     Max
-1.5710 -0.2728 -0.1835 -0.1243 14.1030

Random effects:
Groups  Name                                                Variance Std.Dev. Corr
country (Intercept)                                         0.2204   0.4695
employment.typeCore self-employed                   0.4457   0.6676   -0.20
employment.typeInto core labour force               0.3922   0.6263   -0.35  0.44
employment.typeMarginalized peripheral labour force 0.1228   0.3504   -0.63  0.57  0.39
employment.typePeripheral labour force              0.1090   0.3301   -0.38  0.24  0.70  0.66
employment.typePeripheral self-employed             0.3823   0.6183   -0.32  0.85  0.82  0.66  0.65
Number of obs: 93178, groups:  country, 22

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)                                         -2.817822   0.153843 -18.316  < 2e-16 ***
employment.typeCore self-employed                    1.741686   0.156367  11.138  < 2e-16 ***
employment.typeInto core labour force                0.847817   0.156475   5.418 6.02e-08 ***
employment.typeMarginalized peripheral labour force  1.771534   0.110705  16.002  < 2e-16 ***
employment.typePeripheral labour force               1.021857   0.090266  11.321  < 2e-16 ***
employment.typePeripheral self-employed              1.636287   0.151647  10.790  < 2e-16 ***
gendermale                                           0.153356   0.029485   5.201 1.98e-07 ***
age                                                 -0.008938   0.001540  -5.805 6.44e-09 ***
age.2                                               -3.629799   1.103239  -3.290  0.00100 **
n.adults.minus.n.children                            0.035107   0.010791   3.253  0.00114 **
n.children                                           0.257672   0.028595   9.011  < 2e-16 ***
educationlower secondary                            -0.403009   0.051870  -7.770 7.87e-15 ***
educationupper secondary                            -0.899745   0.049781 -18.074  < 2e-16 ***
educationpost secondary                             -1.584911   0.056888 -27.860  < 2e-16 ***
household.typecouple with children                  -0.117651   0.058688  -2.005  0.04500 *
household.typesingle adult with children             0.512608   0.069332   7.393 1.43e-13 ***
household.typesingle adult without children          0.197551   0.041314   4.782 1.74e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

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