| Type: | Package |
| Title: | R Codes and Datasets for Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup |
| Version: | 0.3.0 |
| Maintainer: | Muhammad Yaseen <myaseen208@gmail.com> |
| Description: | R Codes and Datasets for Stroup, W. W. (2012). Generalized Linear Mixed Models Modern Concepts, Methods and Applications, CRC Press. |
| URL: | https://myaseen208.com/StroupGLMM/ https://CRAN.R-project.org/package=StroupGLMM |
| BugReports: | https://github.com/myaseen208/StroupGLMM/issues |
| Depends: | R (≥ 3.1) |
| Imports: | aod, broom.mixed, car, dplyr, emmeans, ggplot2, lattice, lmerTest, magrittr, MASS, mutoss, nlme, parameters, phia, scatterplot3d, splines, stats, survey |
| License: | GPL-3 |
| LazyData: | true |
| RoxygenNote: | 7.3.2 |
| Encoding: | UTF-8 |
| Note: | 1. School of Mathematical & Statistical Sciences, Clemson University, Clemson, South Carolina, USA 2. Department of Mathematics and Statistics, University of Agriculture Faisalabad, Faisalabad, Pakistan |
| NeedsCompilation: | no |
| Packaged: | 2024-10-01 16:09:18 UTC; myaseen208 |
| Author: | Muhammad Yaseen 
[aut, cre, cph],
Adeela Munawar [aut, ctb],
Walter W. Stroup [aut, ctb],
Kent M. Eskridge [aut, ctb] |
| Repository: | CRAN |
| Date/Publication: | 2024-10-01 22:10:07 UTC |
Data for Example 2.B.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-54)
Description
Exam2.B.2 is used to visualize the effect of glm model statement with binomial data with logit and probit links.
Usage
data(DataExam2.B.2)
Format
A data.frame with 11 rows and 3 variables.
Details
x independent variable
n bernouli trials (bernouli outcomes on each individual)
y number of successes on each individual
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
See Also
Examples
data(DataExam2.B.2)
Data for Example 2.B.3 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-55)
Description
Exam2.B.3 is used to illustrate one way treatment design with Gaussian observations.
Usage
data(DataExam2.B.3)
Format
A data.frame with 6 rows and 2 variables.
Details
trt treatments as factor with number 1 to 3
y response variable
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
See Also
Examples
data(DataExam2.B.3)
Data for Example 2.B.4 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-54)
Description
Exam2.B.4 is used to illustrate one way treatment design with Binomial observations.
Usage
data(DataExam2.B.4)
Format
A data.frame with 6 rows and 4 variables.
Details
obs number of observations
trt three treatments with class factor
Nij number of bernouli trials on each individual
y number of successes on each individual
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
See Also
Examples
data(DataExam2.B.4)
Data for Example 2.B.7 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-60)
Description
Exam2.B.7 is related to multi batch regression data assuming different forms of linear models with factorial experiment.
Usage
data(DataExam2.B.7)
Format
A data.frame with 16 rows and 4 variables.
Details
Rep number of replications
a factor with two levels 1 and 2
b factor with two levels 1 and 2
y response variable
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
See Also
Examples
data(DataExam2.B.7)
Data for Example 3.1 and Example 3.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
DataSet3.1 is used for linear and generalized linear models
Usage
data(DataSet3.1)
Format
A data.frame with 20 rows and 5 variables.
Details
trt two treatment 0 and 1
rep unit of observation or observation ID
Y is continuous & may be assumed Gaussian
N is the number of obs
F is the number of "successes"(N and F specify a binomial response)
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
See Also
Examples
data(DataSet3.1)
DataSt3.2 for Example 3.3, Example 3.4, Example3.6, Example3.8 and Example 3.9 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
DataSet3.2 Multi-Location, 4 Treatment Randomized Block
Usage
data(DataSet3.2)
Format
A data.frame with 32 rows and 10 variables.
Details
trt two treatment 0 and 1
loc four locations used as blocks
Y is Gaussian response variable
Nbin subjects at each Loc x Trt for binomial response
S1 and S2 are two binomial response variables
count1 and count 2 used later
A and B are factors with level 0 and 1
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
See Also
Examples
data(DataSet3.2)
Data for Example3.7 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
Exam1.2 is used to see types of model effects by plotting regression data
Usage
data(DataSet3.3)
Format
A data.frame with 36 rows and 6 variables.
Details
X Each batch observed at several times:0,3,6,12,24,36,48 months
Y continuous variable observed at each level of X
Fav number of successes
N isndependent bernoulli trials
Batch Batches as 1, 2, 3, 4
Count binomial response variable
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
Examples
data(DataSet3.3)
Data for Example 4.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
DataSet4.1 comes from Cochran and Cox (1957) Experimental Design
Usage
data(DataSet4.1)
Format
A data.frame with 60 rows and 3 variables.
Details
blocks 15 blocks in an incomplete block desgin
trt treatments representing incomplete block desgin
y is continuous & may be assumed Gaussian
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
Cochran, W. G., & Cox, G. M. (1957). Experimental designs.
See Also
Examples
data(DataSet4.1)
Data for Example 5.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
DataSet5.1 is used for polynomial multiple regression
Usage
data(DataSet5.1)
Format
A data.frame with 14 rows and 3 variables.
Details
X is predictor variable with level 0, 1, 2, 4, 8, 12, 16
N is the number of independent bernoulli trials for a given observation
F is the number of "successes"(N and F specify a binomial response)
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
See Also
Examples
data(DataSet5.1)
Data for Example 5.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
DataSet5.2 is used for three factor orthogonal main effects only design with sequential fitting of predictors
Usage
data(DataSet5.2)
Format
A data.frame with 9 rows and 4 variables.
Details
a is predictor variable with level 0, 1
b is predictor variable with level 0, 1
c is predictor variable with level 0, 1
y response variable
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
See Also
Examples
data(DataSet5.2)
Data for Example 7.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
Data for Example 7.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Usage
data(DataSet7.1)
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
See Also
Examples
data(DataSet7.1)
Data for Example 7.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
Data for Example 7.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Usage
data(DataSet7.2)
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
See Also
Examples
data(DataSet7.2)
Data for Example 7.3 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
Data for Example 7.3 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Usage
data(DataSet7.3)
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
See Also
Examples
data(DataSet7.3)
Data for Example 7.4 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
Data for Example 7.4 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Usage
data(DataSet7.4)
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
Examples
data(DataSet7.4)
Data for Example 7.4 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
Data for Example 7.4 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Usage
data(DataSet7.4rsm)
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
Examples
data(DataSet7.4rsm)
Data for Example 7.6 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
Data for Example 7.6 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Usage
data(DataSet7.6)
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
See Also
Examples
data(DataSet7.6)
Data for Example 7.7 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
Data for Example 7.7 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Usage
data(DataSet7.7)
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
Examples
data(DataSet7.7)
Data for Example 8.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
DataSet8.1 is used for Nested factorial structure
Usage
data(DataSet8.1)
Format
A data.frame with 30 rows and 4 variables.
Details
block 10 blocks
trt 6 treatments nested within sets
set 2 sets
y is a Gaussian response variable
Author(s)
Muhammad Yaseen (myaseen208@gmail.com) Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear Mixed Models: Modern Concepts, Methods and Applications. CRC press.
See Also
Examples
data(DataSet8.1)
Data for Example 8.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
DataSet8.2 is used for Incomplete strip-plot ( 3 cross 3 factorial).
Usage
data(DataSet8.2)
Format
A data.frame with 36 rows and 6 variables.
Details
block 9 blocks each consisting of 2 rows and 2 coloumns
a is a factor with 3 levels assigned at random to rows
b is a factor with 3 levels assigned at random to columns
y is a Gaussian response variable
Author(s)
Muhammad Yaseen (myaseen208@gmail.com) Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear Mixed Models: Modern Concepts, Methods and Applications. CRC press.
See Also
Examples
data(DataSet8.2)
Data for Example 8.3 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
DataSet8.3 is used for Response surface design with incomplete blocking
Usage
data(DataSet8.3)
Format
A data.frame with 28 rows and 4 variables.
Details
block with 7 blocks
a is a factor with 3 levels 0,-1 and 1
b is a factor with 3 levels 0,-1 and 1
c is a factor with 3 levels 0,-1 and 1
y is a Gaussian response variable
Author(s)
Muhammad Yaseen (myaseen208@gmail.com) Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear Mixed Models: Modern Concepts, Methods and Applications. CRC press.
See Also
Examples
data(DataSet8.3)
Data for Example 8.4 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
DataSet8.4 is used for Multifactor treatment and Multilevel design structures
Usage
data(DataSet8.4)
Format
A data.frame with 36 rows and 6 variables.
Details
block 9 blocks each consisting of 2 rows and 2 coloumns
a is a factor with 3 levels assigned at random to rows
b is a factor with 3 levels assigned at random to columns
y is a Gaussian response variable
Author(s)
Muhammad Yaseen (myaseen208@gmail.com) Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear Mixed Models: Modern Concepts, Methods and Applications. CRC press.
See Also
Examples
data(DataSet8.4)
Data for Example 9.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
DataSet9.1 is used for One-way random effects only model
Usage
data(DataSet9.1)
Format
A data.frame with 24 rows and 2 variables.
Details
a is a factor with 12 levels
y is a Gaussian response variable
Author(s)
Muhammad Yaseen (myaseen208@gmail.com) Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear Mixed Models: Modern Concepts, Methods and Applications. CRC press.
See Also
Examples
data(DataSet9.1)
Data for Example 9.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
DataSet9.2 is used for Two way random effects nested model
Usage
data(DataSet9.2)
Format
A data.frame with 28 rows and 3 variables with levels of b nested within levels of.
Details
a is a factor with 7 levels
b is a factor with 2 levels
y is a Gaussian response variable
Author(s)
Muhammad Yaseen (myaseen208@gmail.com) Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear Mixed Models: Modern Concepts, Methods and Applications. CRC press.
See Also
Examples
data(DataSet9.2)
Data for Example 9.4 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
DataSet9.4 is used for Relationship between BLUP and Fixed Effect Estimators
Usage
data(DataSet9.4)
Format
A data.frame with 32 rows and 3 variables
Details
a is a factor with 2 levels
b is a factor with 8 levels
y is a Gaussian response variable
Author(s)
Muhammad Yaseen (myaseen208@gmail.com) Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear Mixed Models: Modern Concepts, Methods and Applications. CRC press.
See Also
Examples
data(DataSet9.4)
Example1.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-5)
Description
Exam1.1 is used for inspecting probability distribution and to define a plausible process through linear models and generalized linear models.
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
#-------------------------------------------------------------
## Linear Model and results discussed in Article 1.2.1 after Table1.1
#-------------------------------------------------------------
data(Table1.1)
Exam1.1.lm1 <- lm(formula = y/Nx ~ x, data = Table1.1)
summary(Exam1.1.lm1 )
library(parameters)
model_parameters(Exam1.1.lm1)
#-------------------------------------------------------------
## GLM fitting with logit link (family=binomial)
#-------------------------------------------------------------
Exam1.1.glm1 <-
glm(
formula = y/Nx ~ x
, family = binomial(link = "logit")
, data = Table1.1
)
## this glm() function gives warning message of non-integer success
summary(Exam1.1.glm1)
model_parameters(Exam1.1.glm1)
#-------------------------------------------------------------
## GLM fitting with logit link (family = Quasibinomial)
#-------------------------------------------------------------
Exam1.1.glm2 <-
glm(
formula = y/Nx~x
, family = quasibinomial(link = "logit")
, data = Table1.1
)
## problem of "warning message of non-integer success" is overome by using quasibinomial family
summary(Exam1.1.glm2)
model_parameters(Exam1.1.glm2)
#-------------------------------------------------------------
## GLM fitting with survey package(produces same result as using quasi binomial family in glm)
#-------------------------------------------------------------
library(survey)
design <- svydesign(ids = ~1, data = Table1.1)
Exam1.1.svyglm <-
svyglm(
formula = y/Nx~x
, design = design
, family = quasibinomial(link = "logit")
)
summary(Exam1.1.svyglm)
model_parameters(Exam1.1.svyglm)
#-------------------------------------------------------------
## Figure 1.1
#-------------------------------------------------------------
Newdata <-
data.frame(
Table1.1
, LM = Exam1.1.lm1$fitted.values
, GLM = Exam1.1.glm1$fitted.values
, QB = Exam1.1.glm2$fitted.values
, SM = Exam1.1.svyglm$fitted.values
)
#-------------------------------------------------------------
## One Method to plot Figure1.1
#-------------------------------------------------------------
library(ggplot2)
Figure1.1 <-
ggplot(
data = Newdata
, mapping = aes(x = x, y = y/Nx)
) +
geom_point (
mapping = aes(colour = "black")
) +
geom_point (
data = Newdata
, mapping = aes(x = x, y = LM, colour = "blue"), shape = 2
) +
geom_line(
data = Newdata
, mapping = aes(x = x, y = LM, colour = "blue")
) +
geom_point (
data = Newdata
, mapping = aes(x = x, y = GLM, colour ="red"), shape = 3
) +
geom_smooth (
data = Newdata
, mapping = aes(x = x, y = GLM, colour = "red")
, stat = "smooth"
) +
theme_bw() +
scale_colour_manual (
values = c("black", "blue", "red"),
labels = c("observed", "LM", "GLM")
) +
guides (
colour = guide_legend(title = "Plot")
) +
labs (
title = "Linear Model vs Logistic Model"
) +
labs (
y = "p"
)
print(Figure1.1)
#-------------------------------------------------------------
## Another way to plot Figure 1.1
#-------------------------------------------------------------
newdata <-
data.frame(
P = c(
Table1.1$y/Table1.1$Nx
, Exam1.1.lm1$fitted.values
, Exam1.1.glm1$fitted.values
)
, X = rep(Table1.1$x, 3)
, group = rep(c('Obs','LM','GLM'), each = length(Table1.1$x))
)
Figure1.1 <-
ggplot(
data = newdata
, mapping = aes(x = X , y = P)
) +
geom_point(
mapping = aes(x = X , y = P, colour = group , shape=group)
) +
geom_smooth(
data = subset(x = newdata, group == "LM")
, mapping = aes(x=X,y=P)
, col = "green"
) +
geom_smooth(
data = subset(x = newdata, group=="GLM")
, mapping = aes(x = X , y = P)
, col = "red"
) +
theme_bw() +
labs(
title = "Linear Model vs Logistic Model"
)
print(Figure1.1)
#-------------------------------------------------------------
## Correlation among p and fitted values using Gaussian link
#-------------------------------------------------------------
(lmCor <- cor(Table1.1$y/Table1.1$Nx, Exam1.1.lm1$fitted.values))
#-------------------------------------------------------------
## Correlation among p and fitted values using quasi binomial link
#-------------------------------------------------------------
(glmCor <- cor(Table1.1$y/Table1.1$Nx, Exam1.1.glm1$fitted.values))
Example1.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-9)
Description
Exam1.2 is used to see types of model effects by plotting regression data
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
#-------------------------------------------------------------
## Plot of multi-batch regression data discussed in Article 1.3
#-------------------------------------------------------------
data(Table1.1)
Table1.2$Batch <- factor(x = Table1.2$Batch)
library(ggplot2)
Plot <-
ggplot(data = Table1.2, mapping = aes(y = Y, x = X, colour = Batch, shape = Batch)) +
geom_point() +
geom_smooth(method = "lm", fill = NA) +
labs(title = "Plot of Multi Batch Regression data") +
theme_bw()
Plot
Example 2.B.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-53)
Description
Exam2.B.1 is used to visualize the effect of lm model statement with Gaussian data and their design matrix
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
#-----------------------------------------------------------------------------------
## Linear Model discussed in Example 2.B.1 using simple regression data of Table1.1
#-----------------------------------------------------------------------------------
data(Table1.1)
Exam2.B.1.lm1 <- lm(formula = y~x, data = Table1.1)
summary(Exam2.B.1.lm1)
library(parameters)
model_parameters(Exam2.B.1.lm1)
DesignMatrix.lm1 <- model.matrix (object = Exam2.B.1.lm1)
DesignMatrix.lm1
Example 2.B.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-54)
Description
Exam2.B.2 is used to visualize the effect of glm model statement with binomial data with logit and probit links.
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
#-----------------------------------------------------------------------------------
## probitit Model discussed in Example 2.B.2 using DataExam2.B.2
## Default link is logit
## using fmaily = binomial gives warning message of no-integer successes
#-----------------------------------------------------------------------------------
data(DataExam2.B.2)
Exam2.B.2glm <- glm(formula = y/n~x, family = quasibinomial(link = "probit"), data = DataExam2.B.2)
summary(Exam2.B.2glm)
library(parameters)
model_parameters(Exam2.B.2glm)
Example 2.B.3 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-55)
Description
Exam2.B.3 is used to illustrate one way treatment design with Gaussian observations.
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
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)
summary(Exam2.B.3.lm1)
#-----------------------------------------------------------------------------------
## 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)
summary(Exam2.B.3.lm2)
library(parameters)
model_parameters(Exam2.B.3.lm2)
Example 2.B.4 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-56)
Description
Exam2.B.4 is used to illustrate one way treatment design with Binomial observations.
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
#-----------------------------------------------------------------------------------
## logit Model discussed in Example 2.B.2 using DataExam2.B.4
## Default link is logit
## using fmaily=binomial gives warning message of no-integer successes
#-----------------------------------------------------------------------------------
data(DataExam2.B.4)
DataExam2.B.4$trt <- factor(x = DataExam2.B.4$trt)
Exam2.B.4glm <-
glm(
formula = Yij/Nij ~ trt
, family = quasibinomial(link = "probit")
, data = DataExam2.B.4
)
summary(Exam2.B.4glm)
library(parameters)
model_parameters(Exam2.B.4glm)
Example 2.B.5 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-57)
Description
Exam2.B.5 is related to multi batch regression data assuming different forms of linear models.
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
#-----------------------------------------------------------------------------------
## Nested Model with no intercept
#-----------------------------------------------------------------------------------
data(Table1.2)
Table1.2$Batch <- factor(x = Table1.2$Batch)
Exam2.B.5.lm1 <- lm(formula = Y ~ 0 + Batch + Batch/X, data = Table1.2)
DesignMatrix.lm1 <- model.matrix (object = Exam2.B.5.lm1)
DesignMatrix.lm1
#-----------------------------------------------------------------------------------
## Interaction Model with intercept
#-----------------------------------------------------------------------------------
Exam2.B.5.lm2 <-lm(formula = Y ~ Batch + X + Batch*X, data = Table1.2)
DesignMatrix.lm2 <- model.matrix (object = Exam2.B.5.lm2)
DesignMatrix.lm2
#-----------------------------------------------------------------------------------
## Interaction Model with no intercept
#-----------------------------------------------------------------------------------
Exam2.B.5.lm3 <- lm(formula = Y ~ 0 + Batch + Batch*X, data = Table1.2)
DesignMatrix.lm3 <- model.matrix(object = Exam2.B.5.lm3)
DesignMatrix.lm3
#-----------------------------------------------------------------------------------
## Interaction Model with intercept but omitting X term as main effect
#-----------------------------------------------------------------------------------
Exam2.B.5.lm4 <- lm(formula = Y ~ Batch + Batch*X, data = Table1.2)
DesignMatrix.lm4 <- model.matrix(object = Exam2.B.5.lm4)
DesignMatrix.lm4
Example 2.B.6 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-58)
Description
Exam2.B.6 is related to multi batch regression data assuming different forms of linear models keeping batch effect random.
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
#-----------------------------------------------------------------------------------
## Nested Model with no intercept
#-----------------------------------------------------------------------------------
data(Table1.2)
Table1.2$Batch <- factor(x = Table1.2$Batch)
library(nlme)
Exam2.B.6fm1 <- lme(
fixed = Y ~ X
, data = Table1.2
, random = list(Batch = pdDiag(~1), X = pdDiag(~1))
, method = c("REML", "ML")[1]
)
Exam2.B.6fm1
library(broom.mixed)
tidy(Exam2.B.6fm1)
Example 2.B.7 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-60)
Description
Exam2.B.7 is related to multi batch regression data assuming different forms of linear models with factorial experiment.
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
#-----------------------------------------------------------------------------------
## Classical main effects and Interaction Model
#-----------------------------------------------------------------------------------
data(DataExam2.B.7)
DataExam2.B.7$a <- factor(x = DataExam2.B.7$a)
DataExam2.B.7$b <- factor(x = DataExam2.B.7$b)
Exam2.B.7.lm1 <- lm(formula = y~ a + b + a*b, data = DataExam2.B.7)
#-----------------------------------------------------------------------------------
## One way treatment effects model
#-----------------------------------------------------------------------------------
DesignMatrix.lm1 <- model.matrix (object = Exam2.B.7.lm1)
DesignMatrix2.B.7.2 <- DesignMatrix.lm1[,!colnames(DesignMatrix.lm1) %in% c("a2","b")]
lmfit2 <- lm.fit(x = DesignMatrix2.B.7.2, y = DataExam2.B.7$y)
Coefficientslmfit2 <- coef( object = lmfit2)
Coefficientslmfit2
#-----------------------------------------------------------------------------------
## One way treatment effects model without intercept
#-----------------------------------------------------------------------------------
DesignMatrix2.B.7.3 <-
as.matrix(DesignMatrix.lm1[,!colnames(DesignMatrix.lm1) %in% c("(Intercept)","a2","b")])
lmfit3 <- lm.fit(x = DesignMatrix2.B.7.3, y = DataExam2.B.7$y)
Coefficientslmfit3 <- coef( object = lmfit3)
Coefficientslmfit3
#-----------------------------------------------------------------------------------
## Nested Model (both models give the same result)
#-----------------------------------------------------------------------------------
Exam2.B.7.lm4 <- lm(formula = y~ a + a/b, data = DataExam2.B.7)
summary(Exam2.B.7.lm4)
Exam2.B.7.lm4 <- lm(formula = y~ a + a*b, data = DataExam2.B.7)
summary(Exam2.B.7.lm4)
Example 3.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-73)
Description
Exam3.2 used binomial data, two treatment samples
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
#-------------------------------------------------------------
## Linear Model and results discussed in Article 1.2.1 after Table1.1
#-------------------------------------------------------------
data(DataSet3.1)
DataSet3.1$trt <- factor(x = DataSet3.1$trt)
Exam3.2.glm <- glm(formula = F/N~trt, family = quasibinomial(link = "logit"), data = DataSet3.1)
summary(Exam3.2.glm)
library(parameters)
model_parameters(Exam3.2.glm)
#-------------------------------------------------------------
## Individula least squares treatment means
#-------------------------------------------------------------
library(emmeans)
emmeans(object = Exam3.2.glm, specs = "trt")
emmeans(object = Exam3.2.glm, specs = "trt", type = "response")
#---------------------------------------------------
## Over all mean
#---------------------------------------------------
library(phia)
list3.2 <- list(trt = c("0" = 0.5, "1" = 0.5 ))
testFactors(model = Exam3.2.glm, levels = list3.2 )
#---------------------------------------------------
## Repairwise treatment means estimate
#---------------------------------------------------
contrast(emmeans(object = Exam3.2.glm, specs = "trt"))
contrast(emmeans(object = Exam3.2.glm, specs = "trt", type = "response"))
Example 3.3 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-77)
Description
Exam3.3 use RCBD data with fixed location effect and different forms of estimable functions are shown in this example.
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
#-----------------------------------------------------------------------------------
## linear model for Gaussian data
#-----------------------------------------------------------------------------------
data(DataSet3.2)
DataSet3.2$trt <- factor(x = DataSet3.2$trt, level = c(3,0,1,2))
DataSet3.2$loc <- factor(x = DataSet3.2$loc, level = c(8, 1, 2, 3, 4, 5, 6, 7))
levels(DataSet3.2$trt)
levels(DataSet3.2$loc)
Exam3.3.lm1 <- lm(formula = Y~ trt + loc, data = DataSet3.2)
summary( Exam3.3.lm1 )
#-------------------------------------------------------------
## Individual least squares treatment means
#-------------------------------------------------------------
library(emmeans)
(Lsm3.3 <- emmeans(object = Exam3.3.lm1, specs = ~trt))
#---------------------------------------------------
## Pairwise treatment means estimate
#---------------------------------------------------
contrast(object = Lsm3.3 , method = "pairwise")
#---------------------------------------------------
## Revpairwise treatment means estimate
#---------------------------------------------------
contrast(object = Lsm3.3, method = "revpairwise")
#-------------------------------------------------------
## LSM Trt0 (This term is used in Walter Stroups' book)
#-------------------------------------------------------
contrast(
object = emmeans(object = Exam3.3.lm1, specs = ~ trt)
, list(trt = c(0, 1, 0, 0))
)
library(phia)
testFactors(model = Exam3.3.lm1, levels = list(trt = c("0" = 1)))
#-------------------------------------------------------
## LSM Trt0 alt(This term is used in Walter Stroups' book)
#-------------------------------------------------------
# contrast(
# object = emmeans(object = Exam3.3.lm1, specs = ~ trt + loc)
# , list(
# trt = c(0, 1, 0, 0)
# , loc = c(1, 0, 0, 0, 0, 0, 0, 0)
# )
# )
#
#
# list3.3.2 <-
# list(
# trt = c("0" = 1 )
# , loc = c("1" = 0, "2" = 0,"3" = 0,"4" = 0,"5" = 0,"6" = 0,"7" = 0)
# )
# testFactors(model = Exam3.3.lm1, levels = list3.3.2)
#-------------------------------------------------------
## Trt0 Vs Trt1
#-------------------------------------------------------
contrast(
emmeans(object = Exam3.3.lm1, specs = ~trt)
, list(trt = c(0, 1, -1, 0))
)
testFactors(model = Exam3.3.lm1, levels = list(trt = c("0" = 1, "1" = -1)))
#-------------------------------------------------------
## average Trt0 + Trt1
#-------------------------------------------------------
contrast(
emmeans(object = Exam3.3.lm1, specs = ~trt)
, list(trt = c(0, 1/2, 1/2, 0))
)
testFactors(model = Exam3.3.lm1, levels = list(trt = c("0" = 0.5 , "1" = 0.5)))
#-------------------------------------------------------
## average Trt0+2+3
#-------------------------------------------------------
contrast(
emmeans(object = Exam3.3.lm1, specs = ~trt)
, list(trt = c(1/3, 1/3, 0, 1/3))
)
testFactors(model = Exam3.3.lm1, levels = list(trt = c("0" = 1/3,"2" = 1/3,"3" = 1/3)))
#-------------------------------------------------------
## Trt 2 Vs 3 difference
#-------------------------------------------------------
contrast(
emmeans(object = Exam3.3.lm1, specs = ~trt)
, list(trt = c(-1, 0, 0, 1))
)
testFactors(model = Exam3.3.lm1, levels = list(trt = c("2" = 1,"3" = -1)))
#-------------------------------------------------------
## Trt 1 Vs 2 difference
#-------------------------------------------------------
contrast(
emmeans(object = Exam3.3.lm1, specs = ~trt)
, list(trt = c(0, 0, 1, -1))
)
testFactors(model = Exam3.3.lm1, levels = list(trt = c("1" = 1,"2" = -1)))
#-------------------------------------------------------
## Trt 1 Vs 3 difference
#-------------------------------------------------------
contrast(
emmeans(object = Exam3.3.lm1, specs = ~trt)
, list(trt = c(-1, 0, 1, 0))
)
testFactors(model = Exam3.3.lm1, levels = list(trt = c("1" = 1,"3" = -1)))
#-------------------------------------------------------
## Average trt0+1 vs Average Trt2+3
#-------------------------------------------------------
contrast(
emmeans(object = Exam3.3.lm1, specs = ~trt)
, list(trt = c(-1/2, 1/2, 1/2, -1/2))
)
testFactors(model = Exam3.3.lm1, levels = list(trt = c("0" = 0.5,"1" = 0.5,"2" = -0.5,"3" = -0.5)))
#-------------------------------------------------------
## Trt1 vs Average Trt0+1+2
#-------------------------------------------------------
contrast(
emmeans(object = Exam3.3.lm1, specs = ~trt)
, list(trt = c(1/3, 1/3, -1, 1/3))
)
testFactors(model = Exam3.3.lm1, levels = list(trt = c("0" = 1/3,"1" = -1,"2" = 1/3,"3" = 1/3)))
Example 3.5 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-85)
Description
Exam3.5 fixed location, factorial treatment structure, Gaussian response
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
data(DataSet3.2)
DataSet3.2$A <- factor(x = DataSet3.2$A)
DataSet3.2$B <- factor(x = DataSet3.2$B)
DataSet3.2$loc <- factor(x = DataSet3.2$loc, level = c(8, 1, 2, 3, 4, 5, 6, 7))
Exam3.5.lm <- lm(formula = Y~ A + B +loc, data = DataSet3.2)
Exam3.5.lm
##---a0 marginal mean
library(emmeans)
contrast(
object = emmeans(object = Exam3.5.lm, specs = ~ B)
, list(trt = c(1, 0))
)
library(phia)
testFactors(model = Exam3.5.lm, levels = list(B = c("0" = 1,"1" = 0) ))
##---b0 marginal mean
testFactors(model = Exam3.5.lm, levels=list(B = c("0" = 1, "1" = 0)))
##---Simple effect of A on B0
testInteractions(model = Exam3.5.lm, custom = list(B = c("0" = 1,"1" = 0)), across = "B")
##---Simple effect of B on A0
testInteractions(model = Exam3.5.lm, custom = list(A = c("0" = 1, "1" = 0)), across = "A")
##---Simple Effect of A over B
testInteractions(model = Exam3.5.lm, fixed = "A", across = "B")
##---Simple Effect of B over A
testInteractions(model = Exam3.5.lm, fixed = "B", across = "A")
#-------------------------------------------------------------
## Individula least squares treatment means
#-------------------------------------------------------------
emmeans(object = Exam3.5.lm, specs = ~A*B)
Example 3.9 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-118)
Description
Exam3.9 used to differentiate conditional and marginal binomial models with and without interaction for S2 variable.
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
#-----------------------------------------------------------------------------------
## Binomial conditional GLMM without interaction, logit link
#-----------------------------------------------------------------------------------
library(MASS)
DataSet3.2$trt <- factor( x = DataSet3.2$trt )
DataSet3.2$loc <- factor( x = DataSet3.2$loc )
Exam3.9.fm1 <-
glmmPQL(
fixed = S2/Nbin~trt
, random = ~1|loc
, family = quasibinomial(link = "logit")
, data = DataSet3.2
, niter = 10
, verbose = TRUE
)
summary(Exam3.9.fm1)
library(parameters)
model_parameters(Exam3.9.fm1)
#-------------------------------------------------------------
## treatment means
#-------------------------------------------------------------
library(emmeans)
emmeans(object = Exam3.9.fm1, specs = ~trt, type = "response")
emmeans(object = Exam3.9.fm1, specs = ~trt, type = "link")
emmeans(object = Exam3.9.fm1, specs = ~trt, type = "logit")
##--- Normal Approximation
library(nlme)
Exam3.9fm2 <-
lme(
fixed = S2/Nbin~trt
, data = DataSet3.2
, random = ~1|loc
, method = c("REML", "ML")[1]
)
Exam3.9fm2
model_parameters(Exam3.9fm2)
emmeans(object = Exam3.9fm2, specs = ~trt)
##---Binomial GLMM with interaction
Exam3.9fm3 <-
glmmPQL(
fixed = S2/Nbin~trt
, random = ~1|trt/loc
, family = quasibinomial(link = "logit")
, data = DataSet3.2
, niter = 10
, verbose = TRUE
)
summary(Exam3.9fm3)
model_parameters(Exam3.9fm3)
emmeans(object = Exam3.9fm3, specs = ~trt)
##---Binomial Marginal GLMM(assuming compound symmetry)
Exam3.9fm4 <-
glmmPQL(
fixed = S2/Nbin~trt
, random = ~1|loc
, family = quasibinomial(link = "logit")
, data = DataSet3.2
, correlation = corCompSymm(form = ~1|loc)
, niter = 10
, verbose = TRUE
)
summary(Exam3.9fm4)
model_parameters(Exam3.9fm4)
emmeans(object = Exam3.9fm4, specs = ~trt)
Example 4.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-138)
Description
Exam4.1 REML vs ML criterion is used keeping block effects random
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
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)
Exam4.1REML <- lmer(formula = y~ trt +( 1|block ), data = DataSet4.1)
library(parameters)
model_parameters(Exam4.1REML)
print(VarCorr(x = Exam4.1REML), comp = c("Variance"))
##---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)
print(VarCorr(x = Exam4.1ML), comp = c("Variance"))
Exam4.1.lm <- lm(formula = y~ trt + block, data = DataSet4.1)
anova(object = Exam4.1.lm)
Example 5.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-163)
Description
Exam5.1 is used to show polynomial multiple regression with binomial response
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
##---Sequential Fit of the logit Model
Exam5.1.glm.1 <-
glm(
formula = F/N~ X
, family = quasibinomial(link = "logit")
, data = DataSet5.1
)
summary(Exam5.1.glm.1)
library(parameters)
model_parameters(Exam5.1.glm.1)
## confint.default() produce Wald Confidence interval as SAS produces
##---Likelihood Ratio test for Model 1
anova(object = Exam5.1.glm.1, test = "Chisq")
library(aod)
WaldExam5.1.glm.1 <-
wald.test(
Sigma = vcov(object = Exam5.1.glm.1)
, b = coef(object = Exam5.1.glm.1)
, Terms = 2
, L = NULL
, H0 = NULL
, df = NULL
, verbose = FALSE
)
##---Sequential Fit of the logit Model quadratic terms involved
Exam5.1.glm.2 <-
glm(
formula = F/N~ X + I(X^2)
, family = quasibinomial(link = "logit")
, data = DataSet5.1
)
summary( Exam5.1.glm.2 )
model_parameters( Exam5.1.glm.2 )
##---Likelihood Ratio test for Model Exam5.1.glm.2
anova(object = Exam5.1.glm.2, test = "Chisq")
WaldExam5.1.glm.2 <-
wald.test(
Sigma = vcov(object = Exam5.1.glm.2)
, b = coef(object = Exam5.1.glm.2)
, Terms = 3
, L = NULL
, H0 = NULL
, df = NULL
, verbose = FALSE
)
##---Sequential Fit of the logit Model 5th power terms involved
Exam5.1.glm.3 <-
glm(
formula = F/N~ X + I(X^2) + I(X^3) + I(X^4) + I(X^5)
, family = quasibinomial(link = "logit")
, data = DataSet5.1
)
summary(Exam5.1.glm.3)
model_parameters(Exam5.1.glm.3)
## confint.default() produce Wald Confidence interval as SAS produces
##---Likelihood Ratio test for Model 1
anova(object = Exam5.1.glm.3, test = "Chisq")
WaldExam5.1.glm.3 <-
wald.test(
Sigma = vcov(object = Exam5.1.glm.3)
, b = coef(object = Exam5.1.glm.3)
, Terms = 6
, L = NULL
, H0 = NULL
, df = NULL
, verbose = FALSE
)
Example 5.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-164)
Description
Exam5.2 three factor main effects only design
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
DataSet5.2$a <- factor( x = DataSet5.2$a)
DataSet5.2$b <- factor( x = DataSet5.2$b)
DataSet5.2$c <- factor(x = DataSet5.2$c)
##---first adding factor a in model
Exam5.2.lm1 <- lm(formula = y~ a, data = DataSet5.2)
summary(Exam5.2.lm1)
library(parameters)
model_parameters(Exam5.2.lm1)
library(emmeans)
##---A first
emmeans(object = Exam5.2.lm1, specs = ~a)
contrast(emmeans(object = Exam5.2.lm1, specs = ~a), method = "pairwise")
anova(object = Exam5.2.lm1)
##---then adding factor b in model
Exam5.2.lm2 <- lm(formula = y~ a + b, data = DataSet5.2)
summary(Exam5.2.lm2)
model_parameters(Exam5.2.lm2)
emmeans(object = Exam5.2.lm2, specs = ~b)
contrast(emmeans(object = Exam5.2.lm2, specs = ~b), method = "pairwise")
anova(object = Exam5.2.lm2)
##---then adding factor c in model
Exam5.2.lm3 <- lm(formula = y~ a + b + c, data = DataSet5.2)
summary(Exam5.2.lm3)
model_parameters(Exam5.2.lm3)
emmeans(object = Exam5.2.lm3, specs = ~c)
contrast(emmeans(object = Exam5.2.lm3, specs = ~c), method = "pairwise")
anova(object = Exam5.2.lm3)
##---Now Change the order and add b first in model
Exam5.2.lm4 <- lm(formula = y ~ b, data = DataSet5.2)
summary(Exam5.2.lm4)
model_parameters(Exam5.2.lm4)
emmeans(object = Exam5.2.lm4, specs = ~b)
contrast(emmeans(object = Exam5.2.lm4, specs = ~b), method = "pairwise")
anova(object = Exam5.2.lm4)
##---then adding factor a in model
Exam5.2.lm5 <- lm(formula = y ~ b + a, data = DataSet5.2)
summary(Exam5.2.lm5)
model_parameters(Exam5.2.lm5)
emmeans(object = Exam5.2.lm5, specs = ~a)
contrast(emmeans(object = Exam5.2.lm5, specs = ~a), method = "pairwise")
anova(object = Exam5.2.lm5)
Example 5.3 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-172)
Description
Exam5.3 Inference using empirical standard error with different Bias connection
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
data(DataSet4.1)
DataSet4.1$trt <- factor(x = DataSet4.1$trt)
DataSet4.1$block <- factor( x = DataSet4.1$block)
##---REML estimates on page 172
library(lmerTest)
Exam5.3REML <- lmerTest::lmer(formula = y ~ trt + (1|block), data = DataSet4.1, REML = TRUE)
Exam5.3REML
library(parameters)
model_parameters(Exam5.3REML)
##---Standard Error Type "Model Based" with no Bias Connection
anova(object = Exam5.3REML)
anova(object = Exam5.3REML, ddf = "Satterthwaite")
##---Standard Error Type "Model Based" with "Kenward-Roger approximation" Bias Connection
anova(object = Exam5.3REML, ddf = "Kenward-Roger")
##---ML estimates on page 172
Exam5.3ML <- lmerTest::lmer(formula = y ~ trt + ( 1|block ), data = DataSet4.1, REML = FALSE)
Exam5.3ML
library(parameters)
model_parameters(Exam5.3ML)
##---Standard Error Type "Model Based" with no Bias Connection
anova(object = Exam5.3ML )
anova(object = Exam5.3ML, ddf = "Satterthwaite")
Example 7.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-213)
Description
Exam7.1 explains multifactor models with all factors qualitative
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
@seealso
DataSet7.1
Examples
library(emmeans)
library(car)
data(DataSet7.1)
DataSet7.1$a <- factor(x = DataSet7.1$a)
DataSet7.1$b <- factor(x = DataSet7.1$b)
Exam7.1.lm1 <- lm(formula = y ~ a + b + a*b, data = DataSet7.1)
summary(Exam7.1.lm1)
library(parameters)
model_parameters(Exam7.1.lm1)
anova(Exam7.1.lm1)
##---Result obtained as in SLICE statement in SAS for a0 & a1
library(phia)
testInteractions(
model = Exam7.1.lm1
, custom = list(a = c("0" = 1))
, across = "b"
)
testInteractions(
model = Exam7.1.lm1
, custom = list(a = c("1" = 1))
, across = "b"
)
##---Interaction plot
emmip(
object = Exam7.1.lm1
, formula = a~b
, ylab = "y Lsmeans"
, main = "Lsmeans for a*b"
)
#-------------------------------------------------------------
## Individula least squares treatment means
#-------------------------------------------------------------
emmeans(object = Exam7.1.lm1, specs = ~a*b)
##---Simpe effects comparison of interaction by a
## (but it doesn't give the same p-value as in article 7.4.2 page#215)
emmeans(object = Exam7.1.lm1, specs = pairwise~b|a)$contrasts
pairs(emmeans(object = Exam7.1.lm1, specs = ~b|a), simple = "each", combine = TRUE)
pairs(emmeans(object = Exam7.1.lm1, specs = ~b|a), simple = "a")
pairs(emmeans(object = Exam7.1.lm1, specs = ~b|a), simple = "b")
pairs(emmeans(object = Exam7.1.lm1, specs = ~b|a))
contrast(emmeans(object = Exam7.1.lm1, specs = ~b|a))
emmeans(object = Exam7.1.lm1, specs = pairwise~b|a)
emmeans(object = Exam7.1.lm1, specs = pairwise~b|a)$contrasts
##---Alternative method of pairwise comparisons by
## applying contrast
## coefficient (gives the same p-value as in 7.4.2)
contrast(
emmeans(object = Exam7.1.lm1, specs = ~a*b)
, list (
c1 = c(1, 0, -1, 0, 0, 0)
, c2 = c(1, 0, 0, 0, -1, 0)
, c3 = c(0, 0, 1, 0, -1, 0)
, c4 = c(0, 1, 0, -1, 0, 0)
, c5 = c(0, 1, 0, 0, 0, -1)
, c6 = c(0, 1, 0, 0, -1, 0)
)
)
##---Nested Model (page 216)----
Exam7.1.lm2 <- lm(formula = y ~ a + a %in% b, data = DataSet7.1)
summary(Exam7.1.lm2)
model_parameters(Exam7.1.lm2)
anova(Exam7.1.lm2)
car::linearHypothesis(Exam7.1.lm2, c("a0:b1 = a0:b2"))
car::linearHypothesis(Exam7.1.lm2, c("a1:b1 = a1:b2"))
##---Bonferroni's adjusted p-values
emmeans(object = Exam7.1.lm2, specs = pairwise~b|a, adjust = "bonferroni")$contrasts
##--- Alternative method of pairwise comparisons by
## applying contrast coefficient with Bonferroni adjustment
contrast(
emmeans(object = Exam7.1.lm1, specs = ~a*b)
, list (
c1 = c(1, 0, -1, 0, 0, 0)
, c2 = c(1, 0, 0, 0, -1, 0)
, c3 = c(0, 0, 1, 0, -1, 0)
, c4 = c(0, 1, 0, -1, 0, 0)
, c5 = c(0, 1, 0, 0, 0, -1)
, c6 = c(0, 1, 0, 0, -1, 0)
)
, adjust = "bonferroni"
)
Example 7.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-219)
Description
Exam7.2 explains multifactor models with some factors qualitative and some quantitative(Equal slopes ANCOVA)
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
@seealso
DataSet7.2
Examples
library(emmeans)
library(car)
library(ggplot2)
data(DataSet7.2)
DataSet7.2$trt <- factor( x = DataSet7.2$trt )
##----ANCOVA(Equal slope Model)
Exam7.2fm1 <- aov(formula = y ~ trt*x, data = DataSet7.2)
car::Anova(mod = Exam7.2fm1 , type = "III")
##---ANCOVA(without interaction because of non significant slope effect)
Exam7.2fm2 <- aov(formula = y ~ trt + x, data = DataSet7.2)
car::Anova(mod = Exam7.2fm2 , type = "III")
##---Ls means for 2nd model
emmeans(object = Exam7.2fm2, specs = ~trt)
##---Anova without covariate
Exam7.2fm3 <- aov(formula = y ~ trt, data = DataSet7.2)
car::Anova(mod = Exam7.2fm3, type = "III")
##---Ls means for 3rd model
emmeans(object = Exam7.2fm3, specs = ~trt)
##---Box Plot of Covariate by treatment
Plot <-
ggplot(
data = DataSet7.2
, mapping = aes(x = factor(trt), y = x)
) +
geom_boxplot(width = 0.5) +
coord_flip() +
geom_point() +
stat_summary(
fun = "mean"
, geom = "point"
, shape = 23
, size = 2
, fill = "red"
) +
theme_bw() +
ggtitle("Covariate by treatment Box Plot") +
xlab("Treatment")
print(Plot)
Example 7.3 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-223)
Description
Exam7.3 explains multifactor models with some factors qualitative and some quantitative(Unequal slopes ANCOVA)
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
@seealso
DataSet7.3
Examples
library(car)
library(ggplot2)
library(emmeans)
data(DataSet7.3)
DataSet7.3$trt <- factor(x = DataSet7.3$trt )
##----ANCOVA(Unequal slope Model)
Exam7.3fm1 <- aov(formula = y ~ trt*x, data = DataSet7.3)
car::Anova( mod = Exam7.3fm1 , type = "III")
Plot <-
ggplot(
data = DataSet7.3
, mapping = aes(x = factor(trt), y = x)
) +
geom_boxplot(width = 0.5) +
coord_flip() +
geom_point() +
stat_summary(
fun = "mean"
, geom = "point"
, shape = 23
, size = 2
, fill = "red"
) +
theme_bw() +
ggtitle("Covariate by treatment Box Plot") +
xlab("Treatment")
print(Plot)
##----ANCOVA(Unequal slope Model without intercept at page 224)
Exam7.3fm2 <- lm(formula = y ~ 0 + trt/x, data = DataSet7.3)
summary(Exam7.3fm2)
library(parameters)
model_parameters(Exam7.3fm2)
##--Lsmeans treatment at x=7 & 12 at page 225
emmeans(object = Exam7.3fm2, specs = ~trt|x, at = list(x = c(7, 12)))
Example 7.6.2.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-231)
Description
Exam7.6.2.1 Nonlinear Mean Models ( Quantitative by quantitative models)
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
@seealso
DataSet7.6
Examples
library(scatterplot3d)
data(DataSet7.6)
library(dplyr)
library(magrittr)
DataSet7.6 <-
DataSet7.6 %>%
mutate(
logx1 = ifelse(test = x1 == 0, yes = log(x1 + 0.1), no = log(x1))
, logx2 = ifelse(test = x2 == 0, yes = log(x2 + 0.1), no = log(x2))
)
DataSet7.6
Exam7.6.2.1.lm <- lm(formula = response ~ x1*x2 + logx1*logx2 , data = DataSet7.6)
summary(Exam7.6.2.1.lm)
library(parameters)
model_parameters(Exam7.6.2.1.lm)
##---3D Scatter plot ( page#232)
attach(DataSet7.6)
(
ScatterPlot1 <-
scatterplot3d(
x = x1
, y = x2
, z = response
, color = response
, main = " 3D Scatter plot of response")
)
##--- scatter plot with regression plane by using Hoerl function ( page#233)
grid.lines <- 5
x1.pred <- seq(min(x1), max(x1), length.out = grid.lines)
x2.pred <- seq(min(x2), max(x2), length.out = grid.lines)
x1x2 <- expand.grid( x = x1.pred, y = x2.pred)
z.pred <- matrix(data = predict(Exam7.6.2.1.lm, newdata = x1x2),
nrow = grid.lines
, ncol = grid.lines)
(ScatterPlot2 <-
scatterplot3d(
x = x1
, y = x2
, z = response
, pch = 20
, phi = 25
, theta = 30
, ticktype = "detailed"
, xlab = "x1"
, ylab = "x2"
, zlab = "response"
, add = FALSE
, surf = list(x = x1.pred ,
y = x2.pred ,
z = z.pred ,
facets = NA
)
, plot = TRUE
, main = "Fitted Response Surface by Hoerl Function"
)
)
Example 7.7 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-235)
Description
Exam7.7 is an explaination of segmented regression
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
library(splines)
library(ggplot2)
DataSet7.7$a <- factor(x = DataSet7.7$a)
knots <- c(0, 0, 0, 0, 10, 10, 20, 30, 40, 40, 40, 45, 45, 45, 50, 50, 50)
bx <- splineDesign(knots = knots, x = DataSet7.7$x, outer.ok = TRUE)
Exam7.7fm <- lm(formula = y ~ a*bx, data = DataSet7.7)
anova(Exam7.7fm)
Data <- data.frame(DataSet7.7, fit = Exam7.7fm$fit)
##---Estimated response surface by using segmented regression
Plot <-
ggplot(data = Data , mapping = aes(x = x, y = y, colour = a)) +
geom_point() +
geom_line(linewidth = 1) +
ggtitle("Response surface by using segmented regression")
print(Plot)
Example 8.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-250)
Description
Exam8.1 Nested factorial structure
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
data(DataSet8.1)
DataSet8.1$block <- factor(x = DataSet8.1$block)
DataSet8.1$set <- factor(x = DataSet8.1$set)
DataSet8.1$trt <- factor(x = DataSet8.1$trt)
library(lmerTest)
Exam8.1Lmer <- lmer(y ~ set + trt %in% set + (1|set/block), DataSet8.1)
summary(Exam8.1Lmer)
anova(Exam8.1Lmer)
library(emmeans)
emmeans(object = Exam8.1Lmer, specs = ~trt|set)
contrast(emmeans(object = Exam8.1Lmer, specs = ~trt|set), method = "pairwise", by = "set")
Example 8.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-252)
Description
Exam8.2 Incomplete strip-plot
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
data(DataSet8.2)
DataSet8.2$block <- factor(x = DataSet8.2$block)
DataSet8.2$a <- factor(x = DataSet8.2$a)
DataSet8.2$b <- factor(x = DataSet8.2$b)
library(lmerTest)
Exam8.2lmer <-
lmer(
formula = y ~ a*b + (1|block) + (1|block:a) + (1|block:b)
, data = DataSet8.2
)
anova(Exam8.2lmer,ddf="Kenward-Roger")
library(emmeans)
emmeans(object = Exam8.2lmer, specs = ~a|b)
emmip(
object = emmeans(object = Exam8.2lmer, specs = ~a|b)
, formula = a~b
, ylab = "y Lsmeans"
, main = "Lsmeans for a*b"
)
##---Simple effect comparisons of a*b Least Squares Means by a ( page # 254)
emmeans(Exam8.2lmer, pairwise ~ b|a)
Example 8.3 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-255)
Description
Exam8.3 explains Response surface design with incomplete blocking
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
## Response Surface Design with incomplete blocking (page 255)
data(DataSet8.3)
DataSet8.3$block <- factor(x = DataSet8.3$block)
DataSet8.3$aa <- factor(x = DataSet8.3$a)
DataSet8.3$bb <- factor(x = DataSet8.3$b)
DataSet8.3$cc <- factor(x = DataSet8.3$c)
library(lmerTest)
library(lattice)
Exam8.3.fm1 <-
lmer(
y ~ aa:bb:cc + a + b + c +
I(a^2) + I(b^2) + I(c^2) +
a*b + a*c + b*c + (1|block)
, data = DataSet8.3
)
##--- page 256
anova(Exam8.3.fm1, ddf = "Kenward-Roger", type = 1)
Exam8.3.fm2 <-
lmer(
y ~ a + b + c +
I(a^2) + I(b^2) + I(c^2) +
a*b + a*c + b*c + (1|block)
, data = DataSet8.3
)
##--- page 257
anova(Exam8.3.fm2, ddf = "Kenward-Roger", type = 1)
##--- page 257
Exam8.3.fm3 <-
lmer(
y ~ a + b + c +
I(a^2) + I(b^2) +
a*c + b*c + (1|block)
, DataSet8.3
)
anova(Exam8.3.fm3, ddf = "Kenward-Roger", type = 1)
##--- scatter plot with regression plane by using Hoerl function ( page#233)
a <- seq(from = -1, to = 1, by = 1)
b <- seq(from = -1, to = 1, by = 1)
c <- seq(from = -1, to = 1, by = 1)
abc <- expand.grid(a = a, b = b, c = c)
Yhat <- NULL
for(i in 1:nrow(abc)) {
Yhat[i] <- 50.08500 + 1.6*abc$a[i] + 1.69375*abc$b[i] + 0.51875*abc$c[i]-
3.30250*I((abc$a[i])^2)-3.51500*I((abc$b)^2)[i] -
0.52500*(abc$a)[i]*(abc$c)[i]-1.16250*(abc$b)[i]*(abc$c)[i]
}
Newdata <- data.frame(abc, Yhat)
Plot1 <-
wireframe(Yhat ~ b*a, data = subset(Newdata,c==-1),
xlab = "b", ylab = "a",
main = "Predicte response surface at C=-1", colorkey = FALSE,
drape = TRUE, scales = list(arrows = FALSE),xlim=c(max(b),(min(b))),
screen = list(z = -50, x =-70)
)
Plot2 <-
wireframe(Yhat ~ b*a, data = subset(Newdata,c==0),
xlab = "b", ylab = "a",
main = "Predicte response surface at C=0", colorkey = FALSE ,
drape = TRUE, scales = list(arrows = FALSE),xlim=c(max(b),(min(b))),
screen = list(z = -50, x =-70)
)
Plot3 <-
wireframe(Yhat ~ b*a, data = subset(Newdata,c==1),
xlab = "b", ylab = "a",
main = "Predicte response surface at C=1", colorkey = FALSE,
drape = TRUE, scales = list(arrows = FALSE),xlim=c(max(b),(min(b))),
screen = list(z = -50, x =-70)
)
print(Plot1)
print(Plot2)
print(Plot3)
Example 8.4 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-259)
Description
Exam8.4 Multifactor treatment and Multilevel design structures
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
data(DataSet8.4)
DataSet8.4$block <- factor(x = DataSet8.4$block)
DataSet8.4$a <- factor(x = DataSet8.4$a)
DataSet8.4$b <- factor(x = DataSet8.4$b)
library(lmerTest)
Exam8.4lmer <-
lmer(
y ~ a + b %in% a +
(1|block) + (1|block:a) + (1|block:b)
, data = DataSet8.4
)
anova(Exam8.4lmer, ddf = "Kenward-Roger")
library(emmeans)
emmeans(object = Exam8.4lmer, specs = ~a|b)
Example 9.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-273)
Description
Exam9.1 One-way random effects only model
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
data(DataSet9.1)
DataSet9.1$a <- factor(x = DataSet9.1$a)
##---Random effects model
library(lmerTest)
Exam9.1lmer <- lmer( y ~ 1 + (1|a), data = DataSet9.1)
summary(Exam9.1lmer)
##---fixed effects model
Exam9.1lmer2 <- lm(y ~ a, data = DataSet9.1)
summary(Exam9.1lmer2)
#---------------------------------------------------
## Over all mean narrow( page # 274)
#---------------------------------------------------
library(emmeans)
library(phia)
list9.1 <- list(a = c( "1" = 1/12,"2" = 1/12
, "3" = 1/12,"4" = 1/12
, "5" = 1/12,"6" = 1/12
, "7" = 1/12,"8" = 1/12
, "9" = 1/12,"10" = 1/12
, "11" = 1/12,"12" = 1/12
))
phia::testFactors(model = Exam9.1lmer2, levels = list9.1)
#---BLUP Estimates (Table 9.1)
coef <- unlist(ranef(Exam9.1lmer))
BLUPa <- NULL
for( i in 1:length(coef)) {
BLUPa[i] <- (mean(DataSet9.1$y)+coef[i])
}
print(BLUPa)
Example 9.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-276)
Description
Exam9.2 Two way random effects nested model
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
data(DataSet9.2)
DataSet9.2$a <- factor(x = DataSet9.2$a)
DataSet9.2$b <- factor(x = DataSet9.2$b)
library(lmerTest)
Exam9.2lmer <- lmer(y ~ (1|b/a), data = DataSet9.2)
summary(Exam9.2lmer)
Exam9.2lmer2 <- lm(y ~ a + b %in% a, data = DataSet9.2)
summary(Exam9.2lmer2)
##--- Over all mean
library(phia)
list9.2 <- list(a = c("1" = 1/7,"2" = 1/7
, "3" = 1/7,"4" = 1/7
, "5" = 1/7,"6" = 1/7
, "7" = 1/7
))
phia::testFactors(model = Exam9.2lmer2, levels = list9.2)
#---BLUP Estimates
coef <- unlist(ranef(Exam9.2lmer)$a)
BLUPa <- NULL
for(i in 1:length(coef)){
BLUPa[i] <- (mean(DataSet9.2$y) + coef[i])
}
print(BLUPa)
#---BLUP Estimates Narrow
BLUPaNar <- NULL
for( i in 1:length(coef)) {
BLUPaNar[i] <- (mean(DataSet9.2$y) + coef[i])
}
BLUPaNar
Example 9.4 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-288)
Description
Exam9.4 Relationship between BLUP and Fixed Effect Estimators
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
See Also
Examples
data(DataSet9.4)
DataSet9.4$a <- factor(x = DataSet9.4$a)
DataSet9.4$b <- factor(x = DataSet9.4$b)
library(lmerTest)
Exam9.4lmer <- lmer(y ~ a + (1|b) + (1|a/b), data = DataSet9.4)
summary(Exam9.4lmer)
library(emmeans)
emmeans(Exam9.4lmer, spec = ~a)
Data for Table1.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup
Description
Table1.1 is used for inspecting probability distribution and to define a plausible process.
Usage
data(Table1.1)
Format
A data.frame with 11 rows and 3 variables.
Details
x independent variable
Nx bernouli trials (bernouli outcomes on each individual)
y number of successes on each individual
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
Examples
library(StroupGLMM)
data(Table1.1)
Data for Table1.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-10)
Description
Exam1.2 is used to see types of model effects by plotting regression data
Usage
data(Table1.2)
Format
A data.frame with 36 rows and 5 variables.
Details
X have 11 levels in varying intervals from 0 to 48 observed for multiple batches
Y continuous variable observed at each level of X
Fav number of successes
N number of bernoulli trials
Batch Batches as 1, 2, 3, 4
Author(s)
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
References
Stroup, W. W. (2012).Generalized linear mixed models: modern concepts, methods and applications. CRC press.
See Also
Examples
data(Table1.2)