First, I ran the models with on Age as a random and fixed effect. None of the models converged properly. I already suspected this would happen because the models weren’t converging when we add the predictors. I had been modeling the intercept as a random effect

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl =
## control$checkConv, : Model failed to converge with max|grad| = 0.0300648
## (tol = 0.002, component 1)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl =
## control$checkConv, : Model failed to converge with max|grad| = 0.00586908
## (tol = 0.002, component 1)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl =
## control$checkConv, : Model failed to converge with max|grad| = 0.0369218
## (tol = 0.002, component 1)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl =
## control$checkConv, : Model failed to converge with max|grad| = 0.00642891
## (tol = 0.002, component 1)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl =
## control$checkConv, : Model failed to converge with max|grad| = 0.0139171
## (tol = 0.002, component 1)
## boundary (singular) fit: see ?isSingular
## boundary (singular) fit: see ?isSingular
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl =
## control$checkConv, : Model failed to converge with max|grad| = 0.0134041
## (tol = 0.002, component 1)
## boundary (singular) fit: see ?isSingular
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl =
## control$checkConv, : Model failed to converge with max|grad| = 0.00842828
## (tol = 0.002, component 1)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl =
## control$checkConv, : Model failed to converge with max|grad| = 0.00206442
## (tol = 0.002, component 1)
##             DigitSpanFwd_valid DigitSpanBck_valid LogTrailsA LogTrailsB
## (Intercept)            7.15***            5.48***    3.55***    4.78***
## cenAge                -0.02***           -0.02***    0.01***    0.02***
##             FluencyWord_valid BVRtot_valid   LogBVR CVLtca_valid
## (Intercept)          18.72***      8.07***  1.97***     21.08***
## cenAge               -0.05***      0.18***  0.02***     -0.26***
##             CVLfrl_valid CVLfrs_valid Attention_valid
## (Intercept)      6.06***      6.00***         6.41***
## cenAge          -0.11***     -0.12***        -0.03***
## 
## 
## *********************** DigitSpanFwd_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 17004.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.27136 -0.47467 -0.07056  0.43118  2.87479 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr 
##  HNDid    (Intercept) 3.272e+00 1.808823      
##           cenAge      3.141e-05 0.005604 -1.00
##  Residual             1.507e+00 1.227477      
## Number of obs: 4060, groups:  HNDid, 2630
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)  7.148e+00  4.135e-02  2.316e+03 172.858  < 2e-16 ***
## cenAge      -1.978e-02  4.033e-03  3.497e+03  -4.903 9.85e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##        (Intr)
## cenAge 0.165 
## convergence code: 0
## Model failed to converge with max|grad| = 0.0300648 (tol = 0.002, component 1)
## 
## 
## 
## *********************** DigitSpanBck_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 16829.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2976 -0.4149 -0.0695  0.4214  3.8961 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  HNDid    (Intercept) 3.0019   1.73259       
##           cenAge      0.0018   0.04243  -0.19
##  Residual             1.4868   1.21934       
## Number of obs: 4035, groups:  HNDid, 2620
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)  5.482e+00  4.063e-02  2.349e+03 134.929  < 2e-16 ***
## cenAge      -2.007e-02  4.086e-03  1.422e+03  -4.912 1.01e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##        (Intr)
## cenAge 0.138 
## convergence code: 0
## Model failed to converge with max|grad| = 0.00586908 (tol = 0.002, component 1)
## 
## 
## 
## *********************** LogTrailsA ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 4744.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.8297 -0.4305 -0.0597  0.3453  7.1791 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr
##  HNDid    (Intercept) 0.1093565 0.33069      
##           cenAge      0.0001731 0.01316  0.60
##  Residual             0.0911702 0.30194      
## Number of obs: 4273, groups:  HNDid, 2674
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept) 3.554e+00  8.567e-03 2.066e+03  414.85   <2e-16 ***
## cenAge      1.327e-02  8.336e-04 1.366e+03   15.92   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##        (Intr)
## cenAge 0.393 
## convergence code: 0
## Model failed to converge with max|grad| = 0.0369218 (tol = 0.002, component 1)
## 
## 
## 
## *********************** LogTrailsB ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 8581.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1996 -0.4148 -0.1015  0.3383  3.3582 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr
##  HNDid    (Intercept) 4.301e-01 0.65579      
##           cenAge      4.747e-05 0.00689  0.82
##  Residual             1.603e-01 0.40032      
## Number of obs: 4259, groups:  HNDid, 2667
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept) 4.781e+00  1.467e-02 2.238e+03  325.89   <2e-16 ***
## cenAge      2.050e-02  1.353e-03 1.509e+03   15.15   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##        (Intr)
## cenAge 0.306 
## convergence code: 0
## Model failed to converge with max|grad| = 0.00642891 (tol = 0.002, component 1)
## 
## 
## 
## *********************** FluencyWord_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 25558.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1690 -0.5005 -0.0384  0.4437  3.0079 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr 
##  HNDid    (Intercept) 18.738924 4.32885       
##           cenAge       0.001067 0.03267  -1.00
##  Residual              8.977242 2.99620       
## Number of obs: 4299, groups:  HNDid, 2683
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)  1.872e+01  9.729e-02  2.491e+03 192.380  < 2e-16 ***
## cenAge      -5.036e-02  9.595e-03  3.634e+03  -5.248 1.62e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##        (Intr)
## cenAge 0.090 
## convergence code: 0
## Model failed to converge with max|grad| = 0.0139171 (tol = 0.002, component 1)
## 
## 
## 
## *********************** BVRtot_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 24887.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9303 -0.4839 -0.0672  0.4407  4.5770 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr
##  HNDid    (Intercept) 1.482e+01 3.84937      
##           cenAge      8.386e-04 0.02896  1.00
##  Residual             1.076e+01 3.28003      
## Number of obs: 4206, groups:  HNDid, 2656
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept) 8.075e+00  9.411e-02 2.179e+03   85.80   <2e-16 ***
## cenAge      1.818e-01  9.101e-03 3.246e+03   19.98   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##        (Intr)
## cenAge 0.290 
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## 
## 
## 
## *********************** LogBVR ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 9264.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2325 -0.3382  0.1456  0.5298  2.4518 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr 
##  HNDid    (Intercept) 2.040e-01 0.45167       
##           cenAge      9.389e-05 0.00969  -1.00
##  Residual             3.394e-01 0.58260       
## Number of obs: 4206, groups:  HNDid, 2656
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept) 1.968e+00  1.287e-02 2.482e+03  152.91   <2e-16 ***
## cenAge      2.466e-02  1.364e-03 3.046e+03   18.07   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##        (Intr)
## cenAge 0.027 
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## 
## 
## 
## *********************** CVLtca_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 24991.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.70695 -0.54035 -0.00386  0.54855  2.42084 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr 
##  HNDid    (Intercept) 24.212779 4.92065       
##           cenAge       0.002912 0.05396  -0.42
##  Residual             24.589877 4.95882       
## Number of obs: 3761, groups:  HNDid, 2526
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)   21.08334    0.13096 2155.83644  161.00   <2e-16 ***
## cenAge        -0.25638    0.01347 1302.42346  -19.03   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##        (Intr)
## cenAge 0.140 
## convergence code: 0
## Model failed to converge with max|grad| = 0.0134041 (tol = 0.002, component 1)
## 
## 
## 
## *********************** CVLfrl_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 18351.3
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.63021 -0.53023 -0.02366  0.51552  2.46430 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr 
##  HNDid    (Intercept) 5.342e+00 2.31127       
##           cenAge      7.242e-05 0.00851  -1.00
##  Residual             4.188e+00 2.04641       
## Number of obs: 3686, groups:  HNDid, 2491
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)    6.06271    0.05894 2158.52990  102.87   <2e-16 ***
## cenAge        -0.11364    0.00599 2948.16532  -18.97   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##        (Intr)
## cenAge 0.149 
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## 
## 
## 
## *********************** CVLfrs_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 18349.3
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.63905 -0.53843 -0.01732  0.50769  2.48873 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  HNDid    (Intercept) 5.055941 2.24854       
##           cenAge      0.001253 0.03539  -0.18
##  Residual             4.167500 2.04145       
## Number of obs: 3699, groups:  HNDid, 2499
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)  5.997e+00  5.814e-02  2.166e+03  103.14   <2e-16 ***
## cenAge      -1.150e-01  5.952e-03  1.294e+03  -19.33   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##        (Intr)
## cenAge 0.156 
## convergence code: 0
## Model failed to converge with max|grad| = 0.00842828 (tol = 0.002, component 1)
## 
## 
## 
## *********************** Attention_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 15896.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2011 -0.5030  0.0275  0.5181  3.0114 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  HNDid    (Intercept) 2.688832 1.63977      
##           cenAge      0.001596 0.03995  0.22
##  Residual             1.993102 1.41177      
## Number of obs: 3725, groups:  HNDid, 2487
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)  6.414e+00  4.229e-02  2.141e+03 151.656  < 2e-16 ***
## cenAge      -2.784e-02  4.235e-03  1.399e+03  -6.573 6.93e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##        (Intr)
## cenAge 0.236 
## convergence code: 0
## Model failed to converge with max|grad| = 0.00206442 (tol = 0.002, component 1)

Next, I ran the models with on Time as a random and fixed effect. More of the models converged, but several didn’t.

## boundary (singular) fit: see ?isSingular
## boundary (singular) fit: see ?isSingular
## boundary (singular) fit: see ?isSingular
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl =
## control$checkConv, : Model failed to converge with max|grad| = 0.00418018
## (tol = 0.002, component 1)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl =
## control$checkConv, : Model failed to converge with max|grad| = 0.0645692
## (tol = 0.002, component 1)
## boundary (singular) fit: see ?isSingular
## boundary (singular) fit: see ?isSingular
## boundary (singular) fit: see ?isSingular
##             DigitSpanFwd_valid DigitSpanBck_valid LogTrailsA LogTrailsB
## (Intercept)            7.19***            5.53***    3.53***    4.74***
## cenTime               -0.01              -0.02       0.01**     0.02***
##             FluencyWord_valid BVRtot_valid   LogBVR CVLtca_valid
## (Intercept)          18.82***      7.68***  1.92***     21.72***
## cenTime               0.03         0.43***  0.08***     -1.15***
##             CVLfrl_valid CVLfrs_valid Attention_valid
## (Intercept)      6.33***      6.27***         6.47***
## cenTime         -0.38***     -0.36***        -0.05***
## 
## 
## *********************** DigitSpanFwd_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 17027.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.32591 -0.47888 -0.05506  0.45147  2.83677 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr
##  HNDid    (Intercept) 3.3677614 1.83515      
##           cenTime     0.0001259 0.01122  1.00
##  Residual             1.5029957 1.22597      
## Number of obs: 4060, groups:  HNDid, 2630
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)  7.190e+00  4.107e-02  2.600e+03 175.058   <2e-16 ***
## cenTime     -1.144e-02  9.192e-03  1.815e+03  -1.244    0.214    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         (Intr)
## cenTime 0.051 
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## 
## 
## 
## *********************** DigitSpanBck_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 16859.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.3681 -0.3990 -0.0658  0.4113  3.8363 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr 
##  HNDid    (Intercept) 3.2368666 1.79913       
##           cenTime     0.0003629 0.01905  -1.00
##  Residual             1.5055774 1.22702       
## Number of obs: 4035, groups:  HNDid, 2620
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)  5.527e+00  4.053e-02  2.575e+03 136.362   <2e-16 ***
## cenTime     -1.770e-02  9.182e-03  1.831e+03  -1.928    0.054 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         (Intr)
## cenTime -0.015
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## 
## 
## 
## *********************** LogTrailsA ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 5044
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.4990 -0.4141 -0.0537  0.3347  6.9508 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr
##  HNDid    (Intercept) 1.308e-01 0.361610     
##           cenTime     8.367e-05 0.009147 1.00
##  Residual             9.164e-02 0.302726     
## Number of obs: 4273, groups:  HNDid, 2674
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept) 3.530e+00  8.490e-03 2.507e+03 415.782  < 2e-16 ***
## cenTime     6.834e-03  2.151e-03 1.935e+03   3.178  0.00151 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         (Intr)
## cenTime 0.082 
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## 
## 
## 
## *********************** LogTrailsB ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 8740.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0908 -0.2999 -0.0697  0.2526  3.3743 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  HNDid    (Intercept) 0.486374 0.69741      
##           cenTime     0.006696 0.08183  0.11
##  Residual             0.089221 0.29870      
## Number of obs: 4259, groups:  HNDid, 2667
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept) 4.740e+00  1.453e-02 2.622e+03 326.174  < 2e-16 ***
## cenTime     1.930e-02  2.977e-03 1.769e+03   6.484 1.16e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         (Intr)
## cenTime 0.076 
## convergence code: 0
## Model failed to converge with max|grad| = 0.00418018 (tol = 0.002, component 1)
## 
## 
## 
## *********************** FluencyWord_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 25598
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.96183 -0.46513 -0.03612  0.41635  2.81427 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  HNDid    (Intercept) 20.23566 4.4984        
##           cenTime      0.07715 0.2778   -0.06
##  Residual              8.06944 2.8407        
## Number of obs: 4299, groups:  HNDid, 2683
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept) 1.882e+01  9.825e-02 2.678e+03 191.597   <2e-16 ***
## cenTime     3.389e-02  2.143e-02 1.770e+03   1.581    0.114    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         (Intr)
## cenTime -0.010
## 
## 
## *********************** BVRtot_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 24875.7
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.20277 -0.29619 -0.03407  0.26133  2.62348 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  HNDid    (Intercept) 19.503   4.4163        
##           cenTime      0.574   0.7576   -0.06
##  Residual              3.586   1.8938        
## Number of obs: 4206, groups:  HNDid, 2656
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept) 7.682e+00  9.361e-02 2.587e+03   82.06   <2e-16 ***
## cenTime     4.256e-01  2.293e-02 1.916e+03   18.56   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         (Intr)
## cenTime -0.012
## 
## 
## *********************** LogBVR ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 8887.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0644 -0.2782  0.0967  0.3545  2.6882 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  HNDid    (Intercept) 0.35215  0.5934        
##           cenTime     0.01561  0.1249   -0.60
##  Residual             0.13444  0.3667        
## Number of obs: 4206, groups:  HNDid, 2656
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept) 1.920e+00  1.334e-02 2.566e+03  143.90   <2e-16 ***
## cenTime     7.702e-02  3.819e-03 2.188e+03   20.17   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         (Intr)
## cenTime -0.370
## convergence code: 0
## Model failed to converge with max|grad| = 0.0645692 (tol = 0.002, component 1)
## 
## 
## 
## *********************** CVLtca_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 24320
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.50114 -0.47944 -0.02306  0.48124  2.47035 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr
##  HNDid    (Intercept) 30.306430 5.50513      
##           cenTime      0.003695 0.06078  1.00
##  Residual             15.189280 3.89734      
## Number of obs: 3761, groups:  HNDid, 2526
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)   21.72249    0.12815 2481.65496  169.50   <2e-16 ***
## cenTime       -1.15313    0.03088 1708.68173  -37.34   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         (Intr)
## cenTime -0.002
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## 
## 
## 
## *********************** CVLfrl_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 18122.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.60658 -0.48928 -0.03341  0.48927  2.49931 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr
##  HNDid    (Intercept) 6.1699792 2.48394      
##           cenTime     0.0001409 0.01187  1.00
##  Residual             3.3422222 1.82817      
## Number of obs: 3686, groups:  HNDid, 2491
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)    6.33087    0.05890 2438.91523  107.48   <2e-16 ***
## cenTime       -0.38192    0.01461 1695.01151  -26.14   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         (Intr)
## cenTime -0.026
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## 
## 
## 
## *********************** CVLfrs_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 18187.7
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.40502 -0.47576 -0.01688  0.49652  2.53422 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr
##  HNDid    (Intercept) 6.020e+00 2.453510     
##           cenTime     1.876e-05 0.004331 1.00
##  Residual             3.426e+00 1.850874     
## Number of obs: 3699, groups:  HNDid, 2499
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)    6.2692     0.0585 2440.9147  107.16   <2e-16 ***
## cenTime       -0.3650     0.0147 1715.3717  -24.83   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         (Intr)
## cenTime -0.038
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## 
## 
## 
## *********************** Attention_valid ***********************
## 
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: as.formula(merForm)
##    Data: dat
## Control: ..1
## 
## REML criterion at convergence: 15920.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2066 -0.4654  0.0242  0.5259  2.8922 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  HNDid    (Intercept) 2.834399 1.684        
##           cenTime     0.004096 0.064    0.09
##  Residual             1.957670 1.399        
## Number of obs: 3725, groups:  HNDid, 2487
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)    6.47227    0.04139 2433.89171  156.36  < 2e-16 ***
## cenTime       -0.05215    0.01093 1530.95196   -4.77 2.01e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##         (Intr)
## cenTime -0.014

I’m not sure what the best next steps are. Maybe the 3 of us can discuss it briefly during our meeting on Tuesday?