GLMM固定效应与EMM不符：R与Jamovi结果差异原因咨询

我用R的lme4包中glmer函数拟合GLMM时，发现固定效应估计值与估计边际均值（EMM）相差较大，远小于预期。虽然知道固定效应和EMM可能有差异，但我设置的对比编码应该能让系数和EMM匹配，因此怀疑模型有问题。后来用Jamovi的GAMLj包拟合相同GLMM，系数符合预期且与EMM一致，想知道R中glmer结果差异的原因。

缩放对比编码下的GLMM输出结果 #

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: inverse.gaussian  ( identity )
Formula: latency ~ Con_shape * Cue + (1 + Con_shape | subject)
Data: SN_P_PMT_match_data_rt
Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e+05))

     AIC      BIC   logLik deviance df.resid 

81984.2  82071.9 -40979.1  81958.2     6269

Scaled residuals:
Min      1Q  Median      3Q     Max
-3.1154 -0.6553 -0.1732  0.4628  4.9629

Random effects:
Groups   Name               Variance  Std.Dev. Corr  
subject  (Intercept)        1.718e+03 41.44726  
Con_shapeS vs. F   4.076e+03 63.84257  0.02  
Con_shapeS vs. Str 4.896e+03 69.97401  0.18 -0.57
Residual                    7.191e-05  0.00848  
Number of obs: 6282, groups:  subject, 42

Fixed effects:
Estimate Std. Error t value Pr(>|z|)  
(Intercept)                       796.370     14.132  56.354  < 2e-16 ***
Con_shapeS vs. F                   16.932     13.337   1.270    0.204  
Con_shapeS vs. Str                 95.656     15.344   6.234 4.55e-10 ***
CueSad vs Neu                      -3.186      4.045  -0.788    0.431  
Con_shapeS vs. F:CueSad vs Neu     -7.216     10.676  -0.676    0.499  
Con_shapeS vs. Str:CueSad vs Neu   -1.303     11.727  -0.111    0.911
-

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
(Intr) C_Sv.F C_Sv.S CSdvsN C_vFvN
Cn_shpSvs.F  0.088  
Cn_shpSvs.S  0.028 -0.271  
CueSadvsNeu -0.014  0.016  0.001  
C_Sv.F:CSvN -0.096 -0.099 -0.055  0.019  
C_Sv.S:CSvN  0.061  0.129  0.001  0.130 -0.548

估计边际均值（EMM）结果 #

Con_shape Cue       emmean       SE  df asymp.LCL asymp.UCL
self      sad     728.7943 13.14691 Inf  703.0269  754.5618
friend    sad     785.5311 13.31949 Inf  759.4254  811.6369
stranger  sad     811.8101 13.48155 Inf  785.3868  838.2334
self      neutral 733.1200 13.98504 Inf  705.7098  760.5302
friend    neutral 781.1784 14.08376 Inf  753.5748  808.7821
stranger  neutral 810.0302 14.53561 Inf  781.5409  838.5194

缩放对比编码设置 #

#Contrast coding - categorical variables (non-orthogonal)#
contrasts(data$Con_shape) <- cbind("S vs. F"   = c(-.5,.5,0), 
                                   "S vs. Str" = c(-.5,0,.5))

         S vs. F S vs. Str
self        -0.5      -0.5
friend       0.5       0.0
stranger     0.0       0.5

contrasts(data$Cue) <- cbind("Sad vs Neu" = c(-.5,.5))

        Sad vs Neu
sad           -0.5
neutral        0.5

GLMM拟合代码 #

#Run glmer
model <- glmer(latency ~ Con_shape*Cue  +
                          (1+ Con_shape|subject),
                          data=data,
                          family=inverse.gaussian(link="identity"),
                          control=glmerControl
                          (optimizer="bobyqa",optCtrl=list(maxfun=2e5)))

未缩放对比编码的尝试 #

我怀疑差异源于缩放对比编码，于是尝试未缩放编码（-1,1,0），此时效应显著性符合EMM可视化结果，但系数仍差异较大，还出现奇异拟合问题。

未缩放对比编码设置 #

contrasts(SN_P_PMT_data$Con_shape) <- cbind("S vs. F"   = c(-1,1,0), 
                                            "S vs. Str" = c(-1,0,1))
 
contrasts(SN_P_PMT_data$Cue) <- cbind("Sad vs Neu" = c(-1,1)) 

未缩放编码下的GLMM输出结果 #

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: inverse.gaussian  ( identity )
Formula: latency ~ 1 + Con_shape * Cue + (1 + Con_shape | subject)
   Data: SN_P_PMT_match_data_rt
Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e+05))

     AIC      BIC   logLik deviance df.resid 
 82171.8  82259.5 -41072.9  82145.8     6269 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.0716 -0.6663 -0.1754  0.4809  5.3294 

Random effects:
 Groups   Name               Variance  Std.Dev.  Corr     
 subject  (Intercept)        1.734e+03 41.642073          
          Con_shapeS vs. F   5.894e+00  2.427823 1.00     
          Con_shapeS vs. Str 8.270e+02 28.758130 0.19 0.19
 Residual                    7.405e-05  0.008605          
Number of obs: 6282, groups:  subject, 42

Fixed effects:
                                 Estimate Std. Error t value Pr(>|z|)    
(Intercept)                       786.600     13.085  60.113  < 2e-16 ***
Con_shapeS vs. F                   10.198      3.057   3.336 0.000851 ***
Con_shapeS vs. Str                 43.327      8.685   4.989 6.07e-07 ***
CueSad vs Neu                      -1.804      2.118  -0.852 0.394476    
Con_shapeS vs. F:CueSad vs Neu     -1.788      2.972  -0.602 0.547312    
Con_shapeS vs. Str:CueSad vs Neu   -0.504      3.137  -0.161 0.872377    
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) C_Sv.F C_Sv.S CSdvsN C_vFvN
Cn_shpSvs.F  0.220                            
Cn_shpSvs.S  0.127 -0.150                     
CueSadvsNeu -0.004  0.001 -0.007               
C_Sv.F:CSvN  0.001 -0.009  0.013  0.009        
C_Sv.S:CSvN  0.013  0.012 -0.006  0.150 -0.574
optimizer (bobyqa) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')

内容的提问来源于stack exchange，提问作者nalee_psych