title: How to fix singular fit in linear mixed model?
body: <p>I am running a linear mixed model to see if reaction times on a task differ across subject, experimental condition, or target. However, when I run the lme it warns me about singular fit. </p>
  
  <p>I understand that singular fit may indicate an overfitted model, but I don't understand why my models are overfitted with the amount of data I have. </p>
  
  <p>For more information, the experiment involves subjects to name a series of pictures and we record the reaction times (RT). Each participant sees all pictures (targets) and has all 4 conditions. There are 440 targets with 110 targets in each condition. </p>
  
  <p>My first model did not have a singular fit issue:</p>
  
  <pre><code>model1 = lmer(log(RTs300ms)~Condition+(1|Targets)+(1|Subject),data=beh_acc2)
  
  
  REML criterion at convergence: -6030.481
  Random effects:
   Groups   Name        Std.Dev.
   Targets  (Intercept) 0.07918 
   Subject  (Intercept) 0.13678 
   Residual             0.17972 
  Number of obs: 10985, groups:  Targets, 110; Subject, 27
  Fixed Effects:
    (Intercept)    ConditionTh  ConditionUnTa  ConditionUnTh  
        6.67960       -0.03549       -0.01475       -0.01700  
  </code></pre>
  
  <p>But then starting with my second model I started getting the issue:</p>
  
  <pre><code>model2 = lmer(log(RTs300ms)~Condition+(1|Targets)+(1+Condition|Subject),data=beh_acc2)
  
  REML criterion at convergence: -6037.6
  
  Scaled residuals: 
      Min      1Q  Median      3Q     Max 
  -7.3985 -0.6456 -0.1593  0.4551  5.3105 
  
  Random effects:
  Groups   Name          Variance  Std.Dev. Corr             
  Targets  (Intercept)   6.270e-03 0.079184                  
   Subject  (Intercept)   1.947e-02 0.139546                  
            ConditionTh   2.482e-05 0.004982  0.58            
            ConditionUnTa 2.273e-04 0.015078 -0.50  0.41      
            ConditionUnTh 1.200e-04 0.010956 -0.64  0.26  0.99
   Residual               3.226e-02 0.179597                  
  Number of obs: 10985, groups:  Targets, 110; Subject, 27
  
  Fixed effects:
                 Estimate Std. Error t value
  (Intercept)    6.679624   0.028108 237.641
  ConditionTh   -0.035441   0.004949  -7.162
  ConditionUnTa -0.014807   0.005648  -2.621
  ConditionUnTh -0.017071   0.005293  -3.225
  
  Correlation of Fixed Effects:
              (Intr) CndtnT CondtnUnT
  ConditionTh  0.022                 
  ConditinUnT -0.321  0.463          
  ConditnUnTh -0.321  0.471  0.597   
  convergence code: 0
  boundary (singular) fit: see ?isSingular
  </code></pre>
  
  <p>Ideally, I would want my final model to work, but it is the most complex of the three:</p>
  
  <pre><code>model3 = lmer(log(RTs300ms)~Condition+(1+Condition|Targets)+(1+Condition|Subject),data=beh_acc2)
  
  REML criterion at convergence: -6068.3
  
  Scaled residuals: 
      Min      1Q  Median      3Q     Max 
  -7.3684 -0.6393 -0.1575  0.4541  5.2834 
  
  Random effects:
   Groups   Name          Variance  Std.Dev. Corr             
   Targets  (Intercept)   6.931e-03 0.083252                  
            ConditionTh   1.008e-03 0.031748 -0.19            
            ConditionUnTa 1.419e-03 0.037676 -0.35  0.58      
            ConditionUnTh 1.727e-03 0.041553 -0.29  0.72  0.98
   Subject  (Intercept)   1.951e-02 0.139662                  
            ConditionTh   2.575e-05 0.005074  0.57            
            ConditionUnTa 2.371e-04 0.015399 -0.50  0.43      
            ConditionUnTh 1.237e-04 0.011124 -0.63  0.28  0.99
   Residual               3.187e-02 0.178527                  
  Number of obs: 10985, groups:  Targets, 110; Subject, 27
  
  Fixed effects:
                 Estimate Std. Error t value
  (Intercept)    6.679466   0.028234 236.574
  ConditionTh   -0.035074   0.005785  -6.063
  ConditionUnTa -0.014748   0.006706  -2.199
  ConditionUnTh -0.016823   0.006607  -2.546
  
  Correlation of Fixed Effects:
              (Intr) CndtnT CondtnUnT
  ConditionTh -0.008                 
  ConditinUnT -0.325  0.497          
  ConditnUnTh -0.306  0.548  0.722   
  convergence code: 0
  boundary (singular) fit: see ?isSingular
  </code></pre>
  
  <p>I am not sure how to resolve the singular fit issue I get on model2 and model3. I have read some recommendations to try Bayesian models, which I am unfamiliar with. </p>
  
  <p>Any advice or further recommendations on this issue would be greatly appreciated!</p>