[R-sig-ME] singularity issue in lmer

[Catalina Ratala]

Dear List,

I’m trying to make the following model converge without warnings, using the lme4 package:

Variables: Order (3 levels), Valence (2 levels), and Attribute (2 levels) are all factors, Rate is the DV, continuous, 1-10 range.

model_lme4 <- lmer(Rate ~ f_Order*f_Valence + f_Attribute +  (1 + f_Order*f_Valence | Subject), data = data)

summary(model_lme4)

Linear mixed model fit by REML ['lmerMod']
Formula: Rate ~ f_Order * f_Valence + f_Attribute + (1 + f_Order * f_Valence | 
    Subject)
   Data: data
 
REML criterion at convergence: 12167.1
 
Scaled residuals:
    Min      1Q  Median      3Q     Max
-5.0966 -0.5745 -0.0331  0.5851  5.1733
 
Random effects:
 Groups   Name                Variance Std.Dev. Corr                        
 Subject  (Intercept)         0.135654 0.36831                              
          f_Order1            0.002681 0.05178  -0.66                       
          f_Order2            0.003578 0.05982   0.31 -0.92                 
          f_Valence1          0.343519 0.58611   0.35 -0.01 -0.17           
          f_Order1:f_Valence1 0.009916 0.09958  -0.09 -0.49  0.66  0.36     
          f_Order2:f_Valence1 0.001073 0.03276   0.01  0.02 -0.02 -0.88 -0.70
 Residual                     0.974439 0.98714                              
Number of obs: 4237, groups:  Subject, 29
 
Fixed effects:
                      Estimate Std. Error t value
(Intercept)          4.8820728  0.0700895  69.655
f_Order1            -0.0005486  0.0235150  -0.023
f_Order2             0.0220543  0.0241765   0.912
f_Valence1          -1.3284410  0.1099083 -12.087
f_Attribute1         0.0401858  0.0221600   1.813
f_Attribute2        -0.1078952  0.0217247  -4.966
f_Order1:f_Valence1 -0.0157678  0.0283515  -0.556
f_Order2:f_Valence1  0.0552990  0.0223037   2.479
 
Correlation of Fixed Effects:
            (Intr) f_Ord1 f_Ord2 f_Vln1 f_Att1 f_Att2 f_O1:_
f_Order1    -0.263                                         
f_Order2     0.138 -0.578                                   
f_Valence1   0.340 -0.005 -0.077                           
f_Attribut1  0.014 -0.014 -0.024 -0.001                    
f_Attribut2  0.000 -0.007  0.023  0.007 -0.531             
f_Ordr1:_V1 -0.057 -0.131  0.200  0.234  0.016 -0.008      
f_Ordr2:_V1  0.001  0.001 -0.002 -0.237 -0.019  0.027 -0.488
convergence code: 0
boundary (singular) fit: see ?isSingular



My problem is that I get this warning message saying that the model is singular:

boundary (singular) fit: see ?isSingular

 

I used the function isSingular() (package lme4) to test whether actually the warning is valid. It returned TRUE as an outcome, meaning the parameters are on the boundary of the feasible parameter space, and variances of one or more linear combinations of effects are (close to) zero.

I also used allfits() function (afex package) to check whether different optimizers give the same error, which was the case for all the optimizers with which the model converged.

Following different guidelines presented in the literature I tried:

a)     to remove the covariance between random effects, by running the following model:

model_nocov <- lmer(Rate ~ f_Order*f_Valence +  f_Attribute + (0 + f_Order*f_Valence | Subject) + (1 | Subject), data = data);

Linear mixed model fit by REML ['lmerMod']
Formula: Rate ~ f_Order * f_Valence + f_Attribute + (0 + f_Order * f_Valence | 
    Subject) + (1 | Subject)
   Data: data
 
REML criterion at convergence: 11707
 
Scaled residuals:
    Min      1Q  Median      3Q     Max
-5.1014 -0.5736 -0.0361  0.5815  5.1984
 
Random effects:
 Groups    Name                Variance Std.Dev. Corr                        
 Subject   f_Orderfirst        0.000000 0.00000                              
           f_Ordersecond       0.009510 0.09752    NaN                       
           f_Orderthird        0.004304 0.06561    NaN  0.66                 
           f_Valence1          0.105713 0.32514    NaN  0.74  0.68           
           f_Order1:f_Valence1 0.009706 0.09852    NaN  0.83  0.13  0.49     
           f_Order2:f_Valence1 0.001249 0.03534    NaN -0.52 -0.14 -0.82 -0.60
 Subject.1 (Intercept)         0.127141 0.35657                              
 Residual                      0.973996 0.98691                              
Number of obs: 4087, groups:  Subject, 28
 
Fixed effects:
                     Estimate Std. Error t value
(Intercept)          4.873808   0.069807  69.818
f_Order1            -0.005478   0.023784  -0.230
f_Order2             0.028555   0.024044   1.188
f_Valence1          -1.420611   0.063388 -22.411
f_Attribute1         0.048127   0.022588   2.131
f_Attribute2        -0.120467   0.022118  -5.447
f_Order1:f_Valence1 -0.016950   0.028729  -0.590
f_Order2:f_Valence1  0.057331   0.022845   2.510
 
Correlation of Fixed Effects:
            (Intr) f_Ord1 f_Ord2 f_Vln1 f_Att1 f_Att2 f_O1:_
f_Order1    -0.054                                         
f_Order2     0.045 -0.548                                  
f_Valence1   0.103 -0.301  0.255                           
f_Attribut1  0.015 -0.015 -0.025 -0.001                    
f_Attribut2  0.000 -0.004  0.019  0.010 -0.533             
f_Ordr1:_V1  0.053 -0.154  0.260  0.306  0.018 -0.009      
f_Ordr2:_V1 -0.016  0.046 -0.070 -0.233 -0.018  0.028 -0.477
convergence code: 0
boundary (singular) fit: see ?isSingular
 

 

b)     to remove outlier cases;

However, I still got the same warning and the is.singular() indicated that the warnings were to be considered (TRUE).

Moreover, I realized that in this case, what causes the problem are the correlations between the levels of the factor ORDER, which is the one related to my main hypothesis and therefore, I cannot exclude its random slope from the model, as I am interested in its statistical significance and, thus, getting a p-value for it. 

I would like to ask for advice on what I can do to make the model converge without warnings. Is there anything that could be done with the levels of the factor (Order), that seem to be causing the problem? Any other suggestion is, of course, welcomed.



Thank you in advance for your time and help!

 

Best,

Catalina






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