library(hglm.data)Warning: package 'hglm.data' was built under R version 4.3.3Loading required package: MatrixLoading required package: MASSLoading required package: spdata("seeds")Generalized Linear Mixed Models (GLMM)
Persiapan Data
Data yang digunakan perupakan data Seeds genrmination data set dari Crowder (1978) data tersebut ada di package hglm.data:
Menata Data menggunakan package tidyverse
library(tidyverse)
expanded_data <-seeds %>%
mutate(
seed = ifelse(seed == "O75", 0, 1), # 0 jika O75, 1 jika O73
extract = ifelse(extract == "Bean", 0, 1) # 0 jika Bean, 1 jika Cucumber
)
# Menampilkan hasil
print(expanded_data) plate seed extract r n
1 1 0 0 10 39
2 2 0 0 23 62
3 3 0 0 23 81
4 4 0 0 26 51
5 5 0 0 17 39
6 6 1 0 8 16
7 7 1 0 10 30
8 8 1 0 8 28
9 9 1 0 23 45
10 10 1 0 0 4
11 11 0 1 5 6
12 12 0 1 53 74
13 13 0 1 55 72
14 14 0 1 32 51
15 15 0 1 46 79
16 16 0 1 10 13
17 17 1 1 3 12
18 18 1 1 22 41
19 19 1 1 15 30
20 20 1 1 32 51
21 21 1 1 3 7Regresi Logistik
Pemodelan menggunakan regresi logistik sesuai dengan contoh 17.6 pada buku Pawitan halaman 461
data<-data.frame(rr=(seeds$n-seeds$r),expanded_data)
reglog_n<-glm(cbind(r,rr)~extract*seed,family=binomial(link="logit"),data=data)
summary(reglog_n)
Call:
glm(formula = cbind(r, rr) ~ extract * seed, family = binomial(link = "logit"),
data = data)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.5582 0.1260 -4.429 9.46e-06 ***
extract 1.3182 0.1775 7.428 1.10e-13 ***
seed 0.1459 0.2232 0.654 0.5132
extract:seed -0.7781 0.3064 -2.539 0.0111 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 98.719 on 20 degrees of freedom
Residual deviance: 33.278 on 17 degrees of freedom
AIC: 117.87
Number of Fisher Scoring iterations: 4Generalized Linear Mixed Models (GLMM)
library(lme4)
expanded_data$plate<-as.factor(expanded_data$plate)
glmm<-glmer(cbind(r,rr)~seed*extract+(1|plate),family=binomial(link="logit"),data=data)
summary(glmm)Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: binomial ( logit )
Formula: cbind(r, rr) ~ seed * extract + (1 | plate)
Data: data
AIC BIC logLik deviance df.resid
117.5 122.8 -53.8 107.5 16
Scaled residuals:
Min 1Q Median 3Q Max
-1.60042 -0.78762 0.04326 0.72641 1.24275
Random effects:
Groups Name Variance Std.Dev.
plate (Intercept) 0.05503 0.2346
Number of obs: 21, groups: plate, 21
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.54848 0.16608 -3.302 0.000958 ***
seed 0.09743 0.27736 0.351 0.725390
extract 1.33681 0.23618 5.660 1.51e-08 ***
seed:extract -0.81004 0.38417 -2.109 0.034986 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) seed extrct
seed -0.600
extract -0.702 0.412
seed:extrct 0.431 -0.705 -0.617Referensi
Crowder, M. J. 1978. Beta-binomial Anova for proportions, Journal of the Royal Statistical Society (C, Applied Statistics) 27(1), 34–37.
Pawitan, Y. (2001) In All Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford University Press, Oxford.
Bayu, S., Notodiputro, K. A., & Sartono, B. (2023, December). GLMM and GLMMTree for Modelling Poverty in Indonesia. In Proceedings of The International Conference on Data Science and Official Statistics (Vol. 2023, No. 1, pp. 121-131).
McCulloch C.E., Searle S.R. (2001). Generalized, Linear, and Mixed Models. Wiley Series in Probability and Statistics