Description Author(s) References See Also Examples
Exam1.1 is used for inspecting probability distribution and to define a plausible process through linear models and generalized linear models.
Muhammad Yaseen (myaseen208@gmail.com)
Adeela Munawar (adeela.uaf@gmail.com)
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
Table1.1
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)
)
|
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