r - 成功构造 LME4 GLMM 时有所不同 |试验与原始数据？

Question

为什么这些 GLMM 如此不同？

两者都是用 lme4 制作的，都使用相同的数据，但一个是根据成功和试验 (m1bin) 构建的，而一个仅使用原始精度数据 (m1)。我是否完全错误地认为 lme4 从原始数据中找出二项式结构？ (BRMS 做得很好。)现在我担心我的一些分析会改变。

d:
                                                                             uniqueid        dim incorrectlabel accuracy
1 A10LVHTF26QHQC:3X4MXAO0BGONT6U9HL2TG8P9YNBRW8 incidental       marginal        0
2 A10LVHTF26QHQC:3X4MXAO0BGONT6U9HL2TG8P9YNBRW8 incidental        extreme        1
3 A10LVHTF26QHQC:3X4MXAO0BGONT6U9HL2TG8P9YNBRW8   relevant       marginal        1
4 A10LVHTF26QHQC:3X4MXAO0BGONT6U9HL2TG8P9YNBRW8 incidental       marginal        1
5 A10LVHTF26QHQC:3X4MXAO0BGONT6U9HL2TG8P9YNBRW8   relevant       marginal        0
6 A10LVHTF26QHQC:3X4MXAO0BGONT6U9HL2TG8P9YNBRW8 incidental       marginal        0

dbin:
                                                                             uniqueid        dim incorrectlabel right count
                                                                                 <fctr>     <fctr>         <fctr> <int> <int>
1 A10LVHTF26QHQC:3X4MXAO0BGONT6U9HL2TG8P9YNBRW8 incidental        extreme     3     3
2 A10LVHTF26QHQC:3X4MXAO0BGONT6U9HL2TG8P9YNBRW8 incidental       marginal     1     5
3 A10LVHTF26QHQC:3X4MXAO0BGONT6U9HL2TG8P9YNBRW8   relevant        extreme     3     4
4 A10LVHTF26QHQC:3X4MXAO0BGONT6U9HL2TG8P9YNBRW8   relevant       marginal     3     4
5 A16HSMUJ7C7QA7:3DY46V3X3PI4B0HROD2HN770M46557 incidental        extreme     3     4
6 A16HSMUJ7C7QA7:3DY46V3X3PI4B0HROD2HN770M46557 incidental       marginal     2     4

> summary(m1bin)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: cbind(right, count) ~ dim * incorrectlabel + (1 | uniqueid)
     Data: dbin

         AIC      BIC   logLik deviance df.resid 
     398.2    413.5   -194.1    388.2      151 

Scaled residuals: 
         Min       1Q   Median       3Q      Max 
-1.50329 -0.53743  0.08671  0.38922  1.28887 

Random effects:
 Groups   Name        Variance Std.Dev.
 uniqueid (Intercept) 0        0       
Number of obs: 156, groups:  uniqueid, 39

Fixed effects:
                                                                     Estimate Std. Error z value Pr(>|z|)    
(Intercept)                        -0.48460    0.13788  -3.515  0.00044 ***
dimrelevant                        -0.13021    0.20029  -0.650  0.51562    
incorrectlabelmarginal             -0.15266    0.18875  -0.809  0.41863    
dimrelevant:incorrectlabelmarginal -0.02664    0.27365  -0.097  0.92244    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
                        (Intr) dmrlvn incrrc
dimrelevant -0.688              
incrrctlblm -0.730  0.503       
dmrlvnt:ncr  0.504 -0.732 -0.690
> summary(m1)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: accuracy ~ dim * incorrectlabel + (1 | uniqueid)
     Data: d

         AIC      BIC   logLik deviance df.resid 
     864.0    886.2   -427.0    854.0      619 

Scaled residuals: 
        Min      1Q  Median      3Q     Max 
-1.3532 -1.0336  0.7524  0.9350  1.1514 

Random effects:
 Groups   Name        Variance Std.Dev.
 uniqueid (Intercept) 0.04163  0.204   
Number of obs: 624, groups:  uniqueid, 39

Fixed effects:
                                         Estimate Std. Error z value Pr(>|z|)  
(Intercept)          0.140946   0.088242   1.597   0.1102  
dim1                 0.155923   0.081987   1.902   0.0572 .
incorrectlabel1      0.180156   0.081994   2.197   0.0280 *
dim1:incorrectlabel1 0.001397   0.082042   0.017   0.9864  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
                        (Intr) dim1  incrr1
dim1        0.010              
incrrctlbl1 0.128  0.006       
dm1:ncrrct1 0.005  0.138 0.010 

我以为它们是一样的。在 BRMS 中建模可以得到具有相同估计值的相同模型。

Answer 1

它们应该是相同的(直到很小的数值差异:见下文)，除了对数似然和基于它们的度量(尽管一系列模型在对数似然/中存在差异) AIC/等应该是相同的)。我认为您的问题是使用 cbind(right, count) 而不是 cbind(right, count-right):来自 ?glm,

For binomial ... families the response can also be specified as ... a two-column matrix with the columns giving the numbers of successes and failures.

(强调指出这不是成功的次数和总数，而是成功和失败的次数)。

下面是一个使用内置数据集的示例，比较了聚合数据集和分解数据集的拟合情况:

library(lme4)
library(dplyr)

## disaggregate
cbpp_disagg <- cbpp %>% mutate(obs=seq(nrow(cbpp))) %>%
  group_by(obs,herd,period,incidence) %>%
  do(data.frame(disease=rep(c(0,1),c(.$size-.$incidence,.$incidence))))

nrow(cbpp_disagg) == sum(cbpp$size)  ## check

g1 <- glmer(cbind(incidence,size-incidence)~period+(1|herd),
            family=binomial,cbpp)
g2 <- glmer(disease~period+(1|herd),
            family=binomial,cbpp_disagg)

## compare results
all.equal(fixef(g1),fixef(g2),tol=1e-5)
all.equal(VarCorr(g1),VarCorr(g2),tol=1e-6)