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我正在估计一个多级逻辑回归,以预测在给定试验中出错的可能性。该模型具有参与者、场景和参与者的随机效应,以及基于两个变量及其相互作用的固定效应。结果如下:

a1 <- glmer(errorDummy ~ race*object + #fixed effects
  (1|participant) + (1|scenario) + (1|actor), #random effects
  data = df, 
  control = glmerControl(optimizer="bobyqa"),
  family = binomial(link = "logit")) #binomial 
print(summary(a1), correlation = F) #decision to shoot

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: errorDummy ~ race * object + (1 | participant) + (1 | scenario) + (1 | actor)
   Data: df
Control: glmerControl(optimizer = "bobyqa")

     AIC      BIC   logLik deviance df.resid 
  6704.4   6759.2  -3345.2   6690.4    18397 

Scaled residuals: 
   Min     1Q Median     3Q    Max 
-2.557 -0.230 -0.108 -0.045 40.303 

Random effects:
 Groups      Name        Variance Std.Dev.
 participant (Intercept) 0.6115   0.7820  
 actor       (Intercept) 0.8919   0.9444  
 scenario    (Intercept) 1.3102   1.1446  
Number of obs: 18404, groups:  participant, 630; actor, 20; scenario, 8

Fixed effects:
                    Estimate Std. Error z value Pr(>|z|)    
(Intercept)          -4.1705     0.4666  -8.938   <2e-16 ***
raceblack             0.1942     0.4410   0.440     0.66    
objectgun            -2.9482     0.1059 -27.846   <2e-16 ***
raceblack:objectgun  -0.3143     0.2074  -1.516     0.13    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

该模型表明,此任务中的错误并不常见。但是,它们确实因场景而异:

coef(a1)$scenario
              (Intercept) raceblack objectgun raceblack:objectgun
alley           -2.331117 0.1942088 -2.948222          -0.3142849
domesticphone   -3.539802 0.1942088 -2.948222          -0.3142849
grocery         -5.314944 0.1942088 -2.948222          -0.3142849
parkinglot      -4.098250 0.1942088 -2.948222          -0.3142849
pulloverday     -3.084138 0.1942088 -2.948222          -0.3142849
pullovernight   -3.971451 0.1942088 -2.948222          -0.3142849
sidewalk        -5.619601 0.1942088 -2.948222          -0.3142849
warehouse       -4.539444 0.1942088 -2.948222          -0.3142849

我想要的是对比例尺度上八个场景中的每一个的条件模式(最佳线性无偏预测?)的估计。也就是说,我想要估计在给定场景的试验中出错的可能性。

我知道在非多级逻辑回归中为截距执行此操作的公式为 p = exp(logit) / (1 + exp(logit)。这将转化为 p = exp(-4.1705) / (1 + exp(-4.1705)). 但我确信这在具有随机因素的多级上下文中是有问题的。

在给定的场景中,估计在试验中出错的可能性的适当方法是什么?R 中是否有可能内置此功能的软件包?

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