Revisions to Which model for my data?

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edited May 14, 2019 at 17:34

5.2k
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Because your model uses longitudinal data, it is best to check for the Intraclass Correlation Coefficient (ICC) before assuming independence. However, this particualr model has a small sample size, so it is singular,

require(lme4)
my_lme=lmer(Size~Time+(Time|Group),data=my_data,REML=F)
isSingular(my_lme)
[1] TRUE

Let's try using a Bayesian model with a Wishart variance-covariance prior.

    require(blme)
    my_blmer=blmer(cov.prior='wishart',fixef.prior=NULL,resid.prior=NULL,
                   formula=Size~Time+(Time|Group),data=my_data)
isSingular(my_blmer)
[1] FALSE

So it works now, but make sure you can justify the use of a Wishart prior. Let's check the ICC:

    summary(my_blmer)
Cov prior  : Group ~ wishart(df = 4.5, scale = Inf, posterior.scale = cov, common.scale = TRUE)
Prior dev  : -1.4809

Linear mixed model fit by REML ['blmerMod']
Formula: Size ~ Time + (Time | Group)
   Data: my_data

REML criterion at convergence: -7.2

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.74016 -0.23951 -0.04383  0.26814  2.76185 

Random effects:
 Groups   Name        Variance Std.Dev. Corr 
 Group    (Intercept) 0.54671  0.7394        
          Time        0.01784  0.1336   -0.98
 Residual             0.01331  0.1154        
Number of obs: 20, groups:  Group, 3

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.25213    0.43100   0.585
Time         0.06510    0.07882   0.826

Correlation of Fixed Effects:
     (Intr)
Time -0.970

The ICC is quite large: 0.546/(0.546+0.017+0.133)=0.78$0.546/(0.546+0.017+0.133)=0.78$. Thus, you should be using a Hierarchical Linear Model (HLM). Also, because you have a small sample size, you should use a Bayesian HLM.

Because your model uses longitudinal data, it is best to check for the Intraclass Correlation Coefficient (ICC) before assuming independence. However, this particualr model has a small sample size, so it is singular,

require(lme4)
my_lme=lmer(Size~Time+(Time|Group),data=my_data,REML=F)
isSingular(my_lme)
[1] TRUE

Let's try using a Bayesian model with a Wishart variance-covariance prior.

    require(blme)
    my_blmer=blmer(cov.prior='wishart',fixef.prior=NULL,resid.prior=NULL,
                   formula=Size~Time+(Time|Group),data=my_data)
isSingular(my_blmer)
[1] FALSE

So it works now, but make sure you can justify the use of a Wishart prior. Let's check the ICC:

    summary(my_blmer)
Cov prior  : Group ~ wishart(df = 4.5, scale = Inf, posterior.scale = cov, common.scale = TRUE)
Prior dev  : -1.4809

Linear mixed model fit by REML ['blmerMod']
Formula: Size ~ Time + (Time | Group)
   Data: my_data

REML criterion at convergence: -7.2

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.74016 -0.23951 -0.04383  0.26814  2.76185 

Random effects:
 Groups   Name        Variance Std.Dev. Corr 
 Group    (Intercept) 0.54671  0.7394        
          Time        0.01784  0.1336   -0.98
 Residual             0.01331  0.1154        
Number of obs: 20, groups:  Group, 3

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.25213    0.43100   0.585
Time         0.06510    0.07882   0.826

Correlation of Fixed Effects:
     (Intr)
Time -0.970

The ICC is quite large: 0.546/(0.546+0.017+0.133)=0.78. Thus, you should be using a Hierarchical Linear Model (HLM). Also, because you have a small sample size, you should use a Bayesian HLM.

Because your model uses longitudinal data, it is best to check for the Intraclass Correlation Coefficient (ICC) before assuming independence. However, this particualr model has a small sample size, so it is singular,

require(lme4)
my_lme=lmer(Size~Time+(Time|Group),data=my_data,REML=F)
isSingular(my_lme)
[1] TRUE

Let's try using a Bayesian model with a Wishart variance-covariance prior.

require(blme)
my_blmer=blmer(cov.prior='wishart',fixef.prior=NULL,resid.prior=NULL,
               formula=Size~Time+(Time|Group),data=my_data)
isSingular(my_blmer)
[1] FALSE

So it works now, but make sure you can justify the use of a Wishart prior. Let's check the ICC:

summary(my_blmer)
Cov prior  : Group ~ wishart(df = 4.5, scale = Inf, posterior.scale = cov, common.scale = TRUE)
Prior dev  : -1.4809

Linear mixed model fit by REML ['blmerMod']
Formula: Size ~ Time + (Time | Group)
   Data: my_data

REML criterion at convergence: -7.2

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.74016 -0.23951 -0.04383  0.26814  2.76185 

Random effects:
 Groups   Name        Variance Std.Dev. Corr 
 Group    (Intercept) 0.54671  0.7394        
          Time        0.01784  0.1336   -0.98
 Residual             0.01331  0.1154        
Number of obs: 20, groups:  Group, 3

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.25213    0.43100   0.585
Time         0.06510    0.07882   0.826

Correlation of Fixed Effects:
     (Intr)
Time -0.970

The ICC is quite large: $0.546/(0.546+0.017+0.133)=0.78$. Thus, you should be using a Hierarchical Linear Model (HLM). Also, because you have a small sample size, you should use a Bayesian HLM.

Added unabbreviated terms so can be better understood by non-specialists.

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edit approved May 10, 2019 at 20:46

Izy

649
6
21

Because your model uses longitudinal data, it is best to check for the ICCIntraclass Correlation Coefficient (ICC) before assuming independence. However, this particualr model has a small sample size, so it is singular,

require(lme4)
my_lme=lmer(Size~Time+(Time|Group),data=my_data,REML=F)
isSingular(my_lme)
[1] TRUE

Let's try using a Bayesian model with a Wishart variance-covariance prior.

    require(blme)
    my_blmer=blmer(cov.prior='wishart',fixef.prior=NULL,resid.prior=NULL,
                   formula=Size~Time+(Time|Group),data=my_data)
isSingular(my_blmer)
[1] FALSE

So it works now, but make sure you can justify the use of a Wishart prior. Let's check the ICC:

    summary(my_blmer)
Cov prior  : Group ~ wishart(df = 4.5, scale = Inf, posterior.scale = cov, common.scale = TRUE)
Prior dev  : -1.4809

Linear mixed model fit by REML ['blmerMod']
Formula: Size ~ Time + (Time | Group)
   Data: my_data

REML criterion at convergence: -7.2

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.74016 -0.23951 -0.04383  0.26814  2.76185 

Random effects:
 Groups   Name        Variance Std.Dev. Corr 
 Group    (Intercept) 0.54671  0.7394        
          Time        0.01784  0.1336   -0.98
 Residual             0.01331  0.1154        
Number of obs: 20, groups:  Group, 3

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.25213    0.43100   0.585
Time         0.06510    0.07882   0.826

Correlation of Fixed Effects:
     (Intr)
Time -0.970

The ICC is quite large: 0.546/(0.546+0.017+0.133)=0.78. Thus, you should be using an HLMa Hierarchical Linear Model (HLM). Also, because you have a small sample size, you should use a Bayesian HLM.

Because your model uses longitudinal data, it is best to check for the ICC before assuming independence. However, this particualr model has a small sample size, so it is singular,

require(lme4)
my_lme=lmer(Size~Time+(Time|Group),data=my_data,REML=F)
isSingular(my_lme)
[1] TRUE

Let's try using a Bayesian model with a Wishart variance-covariance prior.

    require(blme)
    my_blmer=blmer(cov.prior='wishart',fixef.prior=NULL,resid.prior=NULL,
                   formula=Size~Time+(Time|Group),data=my_data)
isSingular(my_blmer)
[1] FALSE

So it works now, but make sure you can justify the use of a Wishart prior. Let's check the ICC:

    summary(my_blmer)
Cov prior  : Group ~ wishart(df = 4.5, scale = Inf, posterior.scale = cov, common.scale = TRUE)
Prior dev  : -1.4809

Linear mixed model fit by REML ['blmerMod']
Formula: Size ~ Time + (Time | Group)
   Data: my_data

REML criterion at convergence: -7.2

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.74016 -0.23951 -0.04383  0.26814  2.76185 

Random effects:
 Groups   Name        Variance Std.Dev. Corr 
 Group    (Intercept) 0.54671  0.7394        
          Time        0.01784  0.1336   -0.98
 Residual             0.01331  0.1154        
Number of obs: 20, groups:  Group, 3

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.25213    0.43100   0.585
Time         0.06510    0.07882   0.826

Correlation of Fixed Effects:
     (Intr)
Time -0.970

The ICC is quite large: 0.546/(0.546+0.017+0.133)=0.78. Thus, you should be using an HLM. Also, because you have a small sample size, you should use a Bayesian HLM.

Because your model uses longitudinal data, it is best to check for the Intraclass Correlation Coefficient (ICC) before assuming independence. However, this particualr model has a small sample size, so it is singular,

require(lme4)
my_lme=lmer(Size~Time+(Time|Group),data=my_data,REML=F)
isSingular(my_lme)
[1] TRUE

Let's try using a Bayesian model with a Wishart variance-covariance prior.

    require(blme)
    my_blmer=blmer(cov.prior='wishart',fixef.prior=NULL,resid.prior=NULL,
                   formula=Size~Time+(Time|Group),data=my_data)
isSingular(my_blmer)
[1] FALSE

So it works now, but make sure you can justify the use of a Wishart prior. Let's check the ICC:

    summary(my_blmer)
Cov prior  : Group ~ wishart(df = 4.5, scale = Inf, posterior.scale = cov, common.scale = TRUE)
Prior dev  : -1.4809

Linear mixed model fit by REML ['blmerMod']
Formula: Size ~ Time + (Time | Group)
   Data: my_data

REML criterion at convergence: -7.2

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.74016 -0.23951 -0.04383  0.26814  2.76185 

Random effects:
 Groups   Name        Variance Std.Dev. Corr 
 Group    (Intercept) 0.54671  0.7394        
          Time        0.01784  0.1336   -0.98
 Residual             0.01331  0.1154        
Number of obs: 20, groups:  Group, 3

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.25213    0.43100   0.585
Time         0.06510    0.07882   0.826

Correlation of Fixed Effects:
     (Intr)
Time -0.970

The ICC is quite large: 0.546/(0.546+0.017+0.133)=0.78. Thus, you should be using a Hierarchical Linear Model (HLM). Also, because you have a small sample size, you should use a Bayesian HLM.

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created May 10, 2019 at 18:45

Jay Schyler Raadt

1k
7
19

Because your model uses longitudinal data, it is best to check for the ICC before assuming independence. However, this particualr model has a small sample size, so it is singular,

require(lme4)
my_lme=lmer(Size~Time+(Time|Group),data=my_data,REML=F)
isSingular(my_lme)
[1] TRUE

Let's try using a Bayesian model with a Wishart variance-covariance prior.

    require(blme)
    my_blmer=blmer(cov.prior='wishart',fixef.prior=NULL,resid.prior=NULL,
                   formula=Size~Time+(Time|Group),data=my_data)
isSingular(my_blmer)
[1] FALSE

So it works now, but make sure you can justify the use of a Wishart prior. Let's check the ICC:

    summary(my_blmer)
Cov prior  : Group ~ wishart(df = 4.5, scale = Inf, posterior.scale = cov, common.scale = TRUE)
Prior dev  : -1.4809

Linear mixed model fit by REML ['blmerMod']
Formula: Size ~ Time + (Time | Group)
   Data: my_data

REML criterion at convergence: -7.2

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.74016 -0.23951 -0.04383  0.26814  2.76185 

Random effects:
 Groups   Name        Variance Std.Dev. Corr 
 Group    (Intercept) 0.54671  0.7394        
          Time        0.01784  0.1336   -0.98
 Residual             0.01331  0.1154        
Number of obs: 20, groups:  Group, 3

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.25213    0.43100   0.585
Time         0.06510    0.07882   0.826

Correlation of Fixed Effects:
     (Intr)
Time -0.970

The ICC is quite large: 0.546/(0.546+0.017+0.133)=0.78. Thus, you should be using an HLM. Also, because you have a small sample size, you should use a Bayesian HLM.

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