Example 2.B.3 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-55)

Exam2.B.3 is used to illustrate one way treatment design with Gaussian observations.

References

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

See also

DataExam2.B.3

Examples

#-----------------------------------------------------------------------------------
## Means Model  discussed in Example 2.B.3 using DataExam2.B.3
#-----------------------------------------------------------------------------------
Exam2.B.3.lm1 <-
  lm(
      formula     = y~trt
    , data        = DataExam2.B.3
    #  , subset
    #  , weights
    #  , na.action
    , method      = "qr"
    , model       = TRUE
 #  , x           = FALSE
 #  , y           = FALSE
    , qr          = TRUE
    , singular.ok = TRUE
    , contrasts   = NULL
    #  , offset
    #  , ...
  )
summary(Exam2.B.3.lm1)
#> 
#> Call:
#> lm(formula = y ~ trt, data = DataExam2.B.3, method = "qr", model = TRUE, 
#>     qr = TRUE, singular.ok = TRUE, contrasts = NULL)
#> 
#> Residuals:
#>      1      2      3      4      5      6 
#> -0.325 -0.125  1.000 -0.100 -1.275  0.825 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  17.7500     1.0013  17.727 5.95e-05 ***
#> trt           1.5750     0.4635   3.398   0.0273 *  
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.927 on 4 degrees of freedom
#> Multiple R-squared:  0.7427,	Adjusted R-squared:  0.6784 
#> F-statistic: 11.55 on 1 and 4 DF,  p-value: 0.02733
#> 
#-----------------------------------------------------------------------------------
## Effectss Model  discussed in Example 2.B.3 using DataExam2.B.3
#-----------------------------------------------------------------------------------
Exam2.B.3.lm2 <-
  lm(
      formula     = y~0+trt
    , data        = DataExam2.B.3
    #  , subset
    #  , weights
    #  , na.action
    , method      = "qr"
    , model       = TRUE
 #  , x           = FALSE
 #  , y           = FALSE
    , qr          = TRUE
    , singular.ok = TRUE
    , contrasts   = NULL
    #  , offset
    #  , ...
  )
summary(Exam2.B.3.lm2)
#> 
#> Call:
#> lm(formula = y ~ 0 + trt, data = DataExam2.B.3, method = "qr", 
#>     model = TRUE, qr = TRUE, singular.ok = TRUE, contrasts = NULL)
#> 
#> Residuals:
#>      1      2      3      4      5      6 
#>  9.818 10.018  3.536  2.436 -6.346 -4.246 
#> 
#> Coefficients:
#>     Estimate Std. Error t value Pr(>|t|)   
#> trt    9.182      1.398    6.57  0.00123 **
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 7.396 on 5 degrees of freedom
#> Multiple R-squared:  0.8962,	Adjusted R-squared:  0.8754 
#> F-statistic: 43.16 on 1 and 5 DF,  p-value: 0.001226
#>