[R-sig-ME] anova() and the difference between (x | y) and (1 | y:x) in lme4
Ben Bolker
bbolker at gmail.com
Wed Jun 11 16:38:38 CEST 2014
On 14-06-11 10:21 AM, ONKELINX, Thierry wrote:
> Dear Hans,
>
> I assume that var1 is a factor variable.
>
> The difference is in the distribution of the random effects.
>
> (1|var1:var2) : all random intercept come from the same univariate normal distribution rnorm(mean = 0, sd = sigma)
> (0 + var1|var2): the random intercepts come from a multivariate normal distribution: rmvnorm(mean = 0, sigma = Sigma). Sigma is a positive definite matrix
>
> (0 + var1|var2) is a bit easier to understand because the BLUP's have the same interpretation of those of (1|var1:var2)
>
> The bottom-line is that (var1|var2) and (1|var1:var2) allow the same model fit but (var1|var2) makes less assumptions at the cost of estimation more parameters. (var1|var2) requires n * (n + 1) / 2 parameters, with n = number of levels of var1. (1|var1:var2) requires just 1 parameter.
>
> Best regards,
>
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest
> team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
> Kliniekstraat 25
> 1070 Anderlecht
> Belgium
> + 32 2 525 02 51
> + 32 54 43 61 85
> Thierry.Onkelinx at inbo.be
> www.inbo.be
Thanks Tierry.
I would add:
(1) for what it's worth, lme offers an intermediate model (compound
symmetry), which allows for homogeneous but _negative_ within-group
correlation ((1|var1:var2) only allows for non-negative within-group
correlation)
(2) the 'unstructured' (var1|var2) and 'grouped/positive compound
symmetry' models (1|var1:var2) are in principle nested (all
off-diagonals equal to zero, all diagonals identical -> simpler model),
so you should be able to use a likelihood ratio test/ANOVA to test.
(3) your max|grad| convergence warnings are probably false positives;
I would try scaling¢ring your continuous predictors to see if that
makes the eigenvalue warnings go away.
Ben Bolker
>
> To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of.
> ~ Sir Ronald Aylmer Fisher
>
> The plural of anecdote is not data.
> ~ Roger Brinner
>
> The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data.
> ~ John Tukey
>
> -----Oorspronkelijk bericht-----
> Van: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-models-bounces at r-project.org] Namens Hans Ekbrand
> Verzonden: woensdag 11 juni 2014 15:58
> Aan: r-sig-mixed-models at r-project.org
> Onderwerp: [R-sig-ME] anova() and the difference between (x | y) and (1 | y:x) in lme4
>
> 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:
>
> load(url("http://hansekbrand.se/code/my.df.RData"))
>
> 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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