Examp2.4.2.2 from Duchateau, L. and Janssen, P. and Rowlands, G. J. (1998).<em>Linear Mixed Models. An Introduction with applications in Veterinary Research</em>. International Livestock Research Institute.

Examp2.4.2.2 is used for inspecting probability distribution and to define a plausible process through linear models and generalized linear models.
References

Duchateau, L. and Janssen, P. and Rowlands, G. J. (1998).Linear Mixed Models. An Introduction with applications in Veterinary Research. International Livestock Research Institute.
Examples

#-------------------------------------------------------------
## Example 2.4.2.2 p-64
#-------------------------------------------------------------
# PROC MIXED DATA=ex125 METHOD=ML;
# CLASS drug dose region;
# MODEL pcv=drug dose drug*dose;
# RANDOM region drug*region;
# RUN;
# 
# PROC MIXED DATA=ex125 METHOD=REML;
# CLASS drug dose region;
# MODEL pcv=drug dose drug*dose;
# RANDOM region drug*region;
# RUN;


library(lme4)
str(ex125)
#> 'data.frame':	24 obs. of  4 variables:
#>  $ Region: int  1 1 1 1 2 2 2 2 3 3 ...
#>  $ Drug  : Factor w/ 2 levels "BERENIL","samorin": 1 1 2 2 1 1 2 2 1 1 ...
#>  $ dose  : Factor w/ 2 levels "h","l": 1 2 1 2 1 2 1 2 1 2 ...
#>  $ Pcv   : num  22.6 21.8 19.1 16.4 29 28.8 25.3 18.2 24 23.7 ...

fm2.4 <-
  lme4::lmer(
         formula    = Pcv ~ dose*Drug + (1|Region/Drug)
       , data       = ex125
       , REML       = FALSE
       , control    = lmerControl()
       , start      = NULL
       , verbose    = 0L
    #  , subset
    #  , weights
    #  , na.action
    #  , offset
       , contrasts  = NULL
       , devFunOnly = FALSE
    #  , ...
       )
summary(fm2.4)
#> Linear mixed model fit by maximum likelihood  ['lmerMod']
#> Formula: Pcv ~ dose * Drug + (1 | Region/Drug)
#>    Data: ex125
#> 
#>      AIC      BIC   logLik deviance df.resid 
#>    111.9    120.1    -48.9     97.9       17 
#> 
#> Scaled residuals: 
#>      Min       1Q   Median       3Q      Max 
#> -1.87406 -0.56556  0.09217  0.76983  1.27213 
#> 
#> Random effects:
#>  Groups      Name        Variance Std.Dev.
#>  Drug:Region (Intercept) 0.3225   0.5679  
#>  Region      (Intercept) 4.2924   2.0718  
#>  Residual                1.7470   1.3217  
#> Number of obs: 24, groups:  Drug:Region, 12; Region, 6
#> 
#> Fixed effects:
#>                   Estimate Std. Error t value
#> (Intercept)        25.4500     1.0297  24.716
#> dosel              -1.1667     0.7631  -1.529
#> Drugsamorin        -3.9667     0.8306  -4.776
#> dosel:Drugsamorin  -3.1833     1.0792  -2.950
#> 
#> Correlation of Fixed Effects:
#>             (Intr) dosel  Drgsmr
#> dosel       -0.371              
#> Drugsamorin -0.403  0.459       
#> dsl:Drgsmrn  0.262 -0.707 -0.650
anova(fm2.4)
#> Analysis of Variance Table
#>           Df Sum Sq Mean Sq F value
#> dose       1  45.65   45.65 26.1305
#> Drug       1 135.39  135.39 77.4955
#> dose:Drug  1  15.20   15.20  8.7008

fm2.5 <-
  lme4::lmer(
         formula    = Pcv ~ dose*Drug + (1|Region/Drug)
       , data       = ex125
       , REML       = TRUE
       , control    = lmerControl()
       , start      = NULL
       , verbose    = 0L
    #  , subset
    #  , weights
    #  , na.action
    #  , offset
       , contrasts  = NULL
       , devFunOnly = FALSE
    #  , ...
       )
summary(fm2.5)
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Pcv ~ dose * Drug + (1 | Region/Drug)
#>    Data: ex125
#> 
#> REML criterion at convergence: 92.4
#> 
#> Scaled residuals: 
#>      Min       1Q   Median       3Q      Max 
#> -1.71077 -0.51628  0.08414  0.70276  1.16129 
#> 
#> Random effects:
#>  Groups      Name        Variance Std.Dev.
#>  Drug:Region (Intercept) 0.387    0.6221  
#>  Region      (Intercept) 5.151    2.2695  
#>  Residual                2.096    1.4479  
#> Number of obs: 24, groups:  Drug:Region, 12; Region, 6
#> 
#> Fixed effects:
#>                   Estimate Std. Error t value
#> (Intercept)        25.4500     1.1280  22.562
#> dosel              -1.1667     0.8359  -1.396
#> Drugsamorin        -3.9667     0.9098  -4.360
#> dosel:Drugsamorin  -3.1833     1.1822  -2.693
#> 
#> Correlation of Fixed Effects:
#>             (Intr) dosel  Drgsmr
#> dosel       -0.371              
#> Drugsamorin -0.403  0.459       
#> dsl:Drgsmrn  0.262 -0.707 -0.650
anova(fm2.5)
#> Analysis of Variance Table
#>           Df Sum Sq Mean Sq F value
#> dose       1  45.65   45.65 21.7755
#> Drug       1 135.39  135.39 64.5796
#> dose:Drug  1  15.20   15.20  7.2507

library(lmerTest)
#> 
#> Attaching package: ‘lmerTest’
#> The following object is masked from ‘package:lme4’:
#> 
#>     lmer
#> The following object is masked from ‘package:stats’:
#> 
#>     step

fm2.6 <-
    lmerTest::lmer(
         formula    = Pcv ~ dose*Drug + (1|Region/Drug)
        , data       = ex125
        , REML       = FALSE
        , control    = lmerControl()
        , start      = NULL
        , verbose    = 0L
      #	, subset
      #	, weights
      #	, na.action
      #	, offset
        , contrasts  = NULL
        , devFunOnly = FALSE
      #	, ...
        )
summary(fm2.6)
#> Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
#>   method [lmerModLmerTest]
#> Formula: Pcv ~ dose * Drug + (1 | Region/Drug)
#>    Data: ex125
#> 
#>      AIC      BIC   logLik deviance df.resid 
#>    111.9    120.1    -48.9     97.9       17 
#> 
#> Scaled residuals: 
#>      Min       1Q   Median       3Q      Max 
#> -1.87406 -0.56556  0.09217  0.76983  1.27213 
#> 
#> Random effects:
#>  Groups      Name        Variance Std.Dev.
#>  Drug:Region (Intercept) 0.3225   0.5679  
#>  Region      (Intercept) 4.2924   2.0718  
#>  Residual                1.7470   1.3217  
#> Number of obs: 24, groups:  Drug:Region, 12; Region, 6
#> 
#> Fixed effects:
#>                   Estimate Std. Error      df t value Pr(>|t|)    
#> (Intercept)        25.4500     1.0297  9.8496  24.716 3.43e-10 ***
#> dosel              -1.1667     0.7631 12.0000  -1.529 0.152229    
#> Drugsamorin        -3.9667     0.8306 14.1822  -4.776 0.000285 ***
#> dosel:Drugsamorin  -3.1833     1.0792 12.0000  -2.950 0.012151 *  
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Correlation of Fixed Effects:
#>             (Intr) dosel  Drgsmr
#> dosel       -0.371              
#> Drugsamorin -0.403  0.459       
#> dsl:Drgsmrn  0.262 -0.707 -0.650
anova(fm2.6)
#> Type III Analysis of Variance Table with Satterthwaite's method
#>           Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
#> dose       45.65   45.65     1    12 26.1305 0.0002567 ***
#> Drug      135.39  135.39     1     6 77.4955 0.0001192 ***
#> dose:Drug  15.20   15.20     1    12  8.7008 0.0121507 *  
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

fm2.7 <-
    lmerTest::lmer(
         formula    = Pcv ~ dose*Drug + (1|Region/Drug)
        , data       = ex125
        , REML       = TRUE
        , control    = lmerControl()
        , start      = NULL
        , verbose    = 0L
      #	, subset
      #	, weights
      #	, na.action
      #	, offset
        , contrasts  = NULL
        , devFunOnly = FALSE
      #	, ...
        )
summary(fm2.7)
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: Pcv ~ dose * Drug + (1 | Region/Drug)
#>    Data: ex125
#> 
#> REML criterion at convergence: 92.4
#> 
#> Scaled residuals: 
#>      Min       1Q   Median       3Q      Max 
#> -1.71077 -0.51628  0.08414  0.70276  1.16129 
#> 
#> Random effects:
#>  Groups      Name        Variance Std.Dev.
#>  Drug:Region (Intercept) 0.387    0.6221  
#>  Region      (Intercept) 5.151    2.2695  
#>  Residual                2.096    1.4479  
#> Number of obs: 24, groups:  Drug:Region, 12; Region, 6
#> 
#> Fixed effects:
#>                   Estimate Std. Error      df t value Pr(>|t|)    
#> (Intercept)        25.4500     1.1280  8.2080  22.562 1.12e-08 ***
#> dosel              -1.1667     0.8359 10.0000  -1.396 0.193041    
#> Drugsamorin        -3.9667     0.9098 11.8185  -4.360 0.000962 ***
#> dosel:Drugsamorin  -3.1833     1.1822 10.0000  -2.693 0.022594 *  
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Correlation of Fixed Effects:
#>             (Intr) dosel  Drgsmr
#> dosel       -0.371              
#> Drugsamorin -0.403  0.459       
#> dsl:Drgsmrn  0.262 -0.707 -0.650
anova(fm2.7)
#> Type III Analysis of Variance Table with Satterthwaite's method
#>           Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
#> dose       45.65   45.65     1    10 21.7755 0.0008856 ***
#> Drug      135.39  135.39     1     5 64.5796 0.0004826 ***
#> dose:Drug  15.20   15.20     1    10  7.2507 0.0225945 *  
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Examp2.4.2.2 from Duchateau, L. and Janssen, P. and Rowlands, G. J. (1998).Linear Mixed Models. An Introduction with applications in Veterinary Research. International Livestock Research Institute.

References

See also

Examples

Contents

Author
