Example 4.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-138)

Exam4.1 REML vs ML criterion is used keeping block effects random

References

Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.

Author

Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)

Examples


DataSet4.1$trt   <- factor(x =  DataSet4.1$trt)
DataSet4.1$block <- factor(x =  DataSet4.1$block)

#---REML estimates on page 138(article 4.4.3.3)
library(lmerTest)
#> Loading required package: lme4
#> 
#> Attaching package: ‘lme4’
#> The following object is masked from ‘package:nlme’:
#> 
#>     lmList
#> 
#> Attaching package: ‘lmerTest’
#> The following object is masked from ‘package:lme4’:
#> 
#>     lmer
#> The following object is masked from ‘package:stats’:
#> 
#>     step

Exam4.1REML  <- lmer(formula = y~ trt +( 1|block ), data = DataSet4.1)
library(parameters)
model_parameters(Exam4.1REML)
#> # Fixed Effects
#> 
#> Parameter   | Coefficient |   SE |         95% CI | t(43) |      p
#> ------------------------------------------------------------------
#> (Intercept) |       28.18 | 1.66 | [24.82, 31.53] | 16.93 | < .001
#> trt [2]     |       -4.12 | 2.22 | [-8.60,  0.36] | -1.86 | 0.070 
#> trt [3]     |       -3.63 | 2.22 | [-8.10,  0.85] | -1.63 | 0.110 
#> trt [4]     |       -0.34 | 2.22 | [-4.82,  4.14] | -0.15 | 0.880 
#> trt [5]     |       -0.13 | 2.22 | [-4.60,  4.35] | -0.06 | 0.955 
#> trt [6]     |        0.93 | 2.27 | [-3.65,  5.51] |  0.41 | 0.684 
#> trt [7]     |       -0.29 | 2.22 | [-4.76,  4.19] | -0.13 | 0.898 
#> trt [8]     |       -0.36 | 2.22 | [-4.84,  4.12] | -0.16 | 0.872 
#> trt [9]     |        0.74 | 2.22 | [-3.74,  5.22] |  0.33 | 0.741 
#> trt [10]    |       -3.26 | 2.22 | [-7.74,  1.21] | -1.47 | 0.149 
#> trt [11]    |        0.81 | 2.27 | [-3.77,  5.39] |  0.36 | 0.723 
#> trt [12]    |        2.35 | 2.22 | [-2.13,  6.83] |  1.06 | 0.295 
#> trt [13]    |       -2.00 | 2.22 | [-6.48,  2.48] | -0.90 | 0.373 
#> trt [14]    |       -3.26 | 2.22 | [-7.74,  1.22] | -1.47 | 0.149 
#> trt [15]    |        0.42 | 2.22 | [-4.06,  4.90] |  0.19 | 0.852 
#> 
#> # Random Effects
#> 
#> Parameter             | Coefficient |   SE |       95% CI
#> ---------------------------------------------------------
#> SD (Intercept: block) |        2.16 | 0.66 | [1.18, 3.93]
#> SD (Residual)         |        2.93 | 0.37 | [2.28, 3.75]
#> 
#> Uncertainty intervals (equal-tailed) and p-values (two-tailed) computed
#>   using a Wald t-distribution approximation.
print(VarCorr(x = Exam4.1REML), comp = c("Variance"))
#>  Groups   Name        Variance
#>  block    (Intercept) 4.6522  
#>  Residual             8.5559  

##---ML estimates on page 138(article 4.4.3.3)
Exam4.1ML  <- lmer(formula = y ~ trt + (1|block), data = DataSet4.1, REML = FALSE)
model_parameters(Exam4.1ML)
#> # Fixed Effects
#> 
#> Parameter   | Coefficient |   SE |         95% CI | t(43) |      p
#> ------------------------------------------------------------------
#> (Intercept) |       28.23 | 1.44 | [25.33, 31.12] | 19.66 | < .001
#> trt [2]     |       -4.16 | 1.88 | [-7.95, -0.37] | -2.21 | 0.032 
#> trt [3]     |       -3.68 | 1.88 | [-7.47,  0.11] | -1.96 | 0.057 
#> trt [4]     |       -0.58 | 1.88 | [-4.37,  3.21] | -0.31 | 0.760 
#> trt [5]     |       -0.17 | 1.88 | [-3.96,  3.62] | -0.09 | 0.927 
#> trt [6]     |        0.87 | 1.93 | [-3.02,  4.75] |  0.45 | 0.655 
#> trt [7]     |       -0.37 | 1.88 | [-4.16,  3.42] | -0.20 | 0.844 
#> trt [8]     |       -0.35 | 1.88 | [-4.14,  3.44] | -0.19 | 0.851 
#> trt [9]     |        0.76 | 1.88 | [-3.03,  4.55] |  0.41 | 0.686 
#> trt [10]    |       -3.27 | 1.88 | [-7.06,  0.52] | -1.74 | 0.089 
#> trt [11]    |        0.68 | 1.93 | [-3.21,  4.56] |  0.35 | 0.728 
#> trt [12]    |        2.22 | 1.88 | [-1.57,  6.01] |  1.18 | 0.243 
#> trt [13]    |       -1.95 | 1.88 | [-5.74,  1.84] | -1.04 | 0.305 
#> trt [14]    |       -3.24 | 1.88 | [-7.03,  0.55] | -1.72 | 0.092 
#> trt [15]    |        0.35 | 1.88 | [-3.44,  4.14] |  0.18 | 0.855 
#> 
#> # Random Effects
#> 
#> Parameter             | Coefficient |   SE |       95% CI
#> ---------------------------------------------------------
#> SD (Intercept: block) |        2.12 | 0.52 | [1.31, 3.44]
#> SD (Residual)         |        2.46 | 0.26 | [2.00, 3.02]
#> 
#> Uncertainty intervals (equal-tailed) and p-values (two-tailed) computed
#>   using a Wald t-distribution approximation.
print(VarCorr(x =  Exam4.1ML), comp = c("Variance"))
#>  Groups   Name        Variance
#>  block    (Intercept) 4.5030  
#>  Residual             6.0371  

Exam4.1.lm <- lm(formula  = y~ trt + block, data = DataSet4.1)
anova(object = Exam4.1.lm)
#> Analysis of Variance Table
#> 
#> Response: y
#>           Df Sum Sq Mean Sq F value   Pr(>F)   
#> trt       14 299.43 21.3881  2.4825 0.017187 * 
#> block     14 333.42 23.8159  2.7643 0.009004 **
#> Residuals 31 267.08  8.6154                    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Example 4.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-138)

References

See also

Author

Examples