# Exam1.1: Example1.1 from Generalized Linear Mixed Models: Modern... In StroupGLMM: R Codes and Datasets for Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup

## Description

Exam1.1 is used for inspecting probability distribution and to define a plausible process through linear models and generalized linear models.

## References

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

`Table1.1`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212``` ```#------------------------------------------------------------- ## 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 # , subset # , weights # , na.action , method = "qr" , model = TRUE , x = FALSE , y = FALSE , qr = TRUE , singular.ok = TRUE , contrasts = NULL # , offset # , ... ) summary(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 , weights = NULL # , subset # , na.action , start = NULL # , etastart # , mustart # , offset # , control = list(...) # , model = TRUE , method = "glm.fit" , x = FALSE , y = TRUE , contrasts = NULL # , ... ) ## this glm() function gives warning message of non-integer success summary(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 , weights = NULL # , subset # , na.action , start = NULL # , etastart # , mustart # , offset # , control = list(...) # , model = TRUE , method = "glm.fit" , x = FALSE , y = TRUE , contrasts = NULL # , ... ) ## problem of "warning message of non-integer success" is overome by using quasibinomial family summary(Exam1.1.glm2) #------------------------------------------------------------- ## GLM fitting with survey package(produces same result as using quasi binomial family in glm) #------------------------------------------------------------- library(survey) design <- svydesign( ids = ~1 , probs = NULL , strata = NULL , variables = NULL , fpc = NULL , data = Table1.1 # , nest = FALSE # , check.strata = !nest , weights = NULL , pps = FALSE # , ... ) Exam1.1.svyglm <- svyglm( formula = y/Nx~x , design = design # , ... , family = quasibinomial(link="logit") ) # summary(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) ) ```

### Example output

```Call:
lm(formula = y/Nx ~ x, data = Table1.1, method = "qr", model = TRUE,
x = FALSE, y = FALSE, qr = TRUE, singular.ok = TRUE, contrasts = NULL)

Residuals:
Min       1Q   Median       3Q      Max
-0.18995 -0.09450  0.05671  0.08904  0.10883

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.08944    0.06625  -1.350     0.21
x            0.11152    0.01120   9.958 3.71e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1175 on 9 degrees of freedom
Multiple R-squared:  0.9168,	Adjusted R-squared:  0.9075
F-statistic: 99.16 on 1 and 9 DF,  p-value: 3.706e-06

Warning message:
In eval(family\$initialize) : non-integer #successes in a binomial glm!

Call:
glm(formula = y/Nx ~ x, family = binomial(link = "logit"), data = Table1.1,
weights = NULL, start = NULL, method = "glm.fit", x = FALSE,
y = TRUE, contrasts = NULL)

Deviance Residuals:
Min        1Q    Median        3Q       Max
-0.30433  -0.22562   0.04623   0.09882   0.44188

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)  -3.9082     2.3234  -1.682   0.0925 .
x             0.7287     0.4057   1.796   0.0725 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 7.45149  on 10  degrees of freedom
Residual deviance: 0.67672  on  9  degrees of freedom
AIC: 8.3671

Number of Fisher Scoring iterations: 5

Call:
glm(formula = y/Nx ~ x, family = quasibinomial(link = "logit"),
data = Table1.1, weights = NULL, start = NULL, method = "glm.fit",
x = FALSE, y = TRUE, contrasts = NULL)

Deviance Residuals:
Min        1Q    Median        3Q       Max
-0.30433  -0.22562   0.04623   0.09882   0.44188

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  -3.9082     0.6366  -6.139 0.000171 ***
x             0.7287     0.1112   6.555 0.000105 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for quasibinomial family taken to be 0.07508072)

Null deviance: 7.45149  on 10  degrees of freedom
Residual deviance: 0.67672  on  9  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 5

Attaching package: 'survey'

The following object is masked from 'package:graphics':

dotchart

`geom_smooth()` using method = 'loess' and formula 'y ~ x'
`geom_smooth()` using method = 'loess' and formula 'y ~ x'
`geom_smooth()` using method = 'loess' and formula 'y ~ x'
[1] 0.9574927
[1] 0.9810858
```

StroupGLMM documentation built on May 2, 2019, 9:42 a.m.