Count data are most commonly modeled using the Poisson model, or by one of its many extensions. In this study, a Poisson generalized linear mixed model (GLMM) with spatio-temporal random effects was modeled using two approaches. They are conditional autoregressive linear models and conditional autoregressive adaptive models. The models in this paper are fitted in a Bayesian setting using Markov chain Monte Carlo simulation. All parameters whose full conditional distributions have a closed-form distribution are Gibbs sampled, which includes the regression parameters and the random effects, as well as the variance parameters in all models. The models are applied to child labor in Sumatra between 2014 and 2017. Our main results show that the unemployment rate, illiteracy rates, and dropout rates influence the child labor number in Sumatra. Of the two models used, the spatio-temporal model with CAR adaptive is the best model by producing a simpler model but requires more time to build the model.

1.
Lee
D.
,
Rushworth
,
A.
, and
Napler
,
G.
Spatio Temporal Area Unit Modeling in R with Conditional Autoregressive Priors Using The CARBayesST Package
”.
Journal of Statistical Software.
Vol.
84
. Issue
9
. (
2018
).
2.
Li
G.
,
Best
N.
,
Hansell
A.
,
Ahmed
I.
, and
Richardson
S.
BaySTDetect: Detecting Unusual Temporal Patterns in Small Area Data via Bayesian Model Choice
.”
Biostatistics
,
13
(
4
),
695
710
. (
2012
).
3.
Lee
D.
, and
Lawson
A.
Quantifying the Spatial Inequality and Temporal Trends in Maternal Smoking Rates in Glasgow
”.
The Annals of Applied Statistics
,
10
(
3
),
1427
1446
. (
2016
).
4.
Sammatat
,
Sunaee
and
Lakdee
Krisada
. “
Generalized Linear Mixed Models for Spatio-Temporal Data with an Applicaltion to Leptospirosis in Thailand
”.
Applied Mathematical Sciences.
Vol.
12
. (
2018
).
5.
Bernardinelli
L.
,
Clayton
D.
,
Pascutto
C.
,
Montomoli
C.
,
Ghislandi
M.
, and
Songini
M.
Bayesian Analysis of Space-Time Variation in Disease Risk
”.
Statistics in Medicine
,
14
,
2433
2443
. (
2000
).
6.
Knorr-Held
L.
Bayesian Modelling of Inseparable Space-Time Variation in Disease Risk
.”
Statistics in Medicine
,
19
(
17–18
),
2555
2567
. (
2000
).
7.
Banerjee
,
S.
,
Carlin
,
B.
, and
Gelfand
,
A.
Hierarchical Modeling and Analysis for Spatial Data
”.
Boca Raton: Chapman & Hall.
(
2004
).
8.
Napier
G.
,
Lee
D.
,
Robertson
C.
,
Lawson
A.
, and
Pollock
K.
A Model to Estimate the Impact of Changes in MMR Vaccination Uptake on Inequalities in Measles Susceptibility in Scotland
.”
Statistical Methods in Medical Research
,
25
(
4
),
1185
1200
. (
2016
).
9.
Rushworth
A.
,
Lee
D.
, and
Mitchell
R.
A Spatio-Temporal Model for Estimating the Long-Term Effects of Air Pollution on Respiratory Hospital Admissions in Greater London
”.
Spatial and Spatio-Temporal Epidemiology
,
10
,
29
38
. (
2014
).
10.
Rushworth
A.
,
Lee
D.
, and
Sarran
C.
An Adaptive Spatio-Temporal Smoothing Model for Estimating Trends and Step Changes in Disease Risk
”.
Journal of the Royal Statistical Society C.
,
66
(
1
),
141
157
. (
2017
).
11.
Besag
,
J. E.
Statistical analysis of non-lattice data
”.
The Statistician
24
,
179
195
. (
1975
).
12.
Cressie
,
N. A. C.
, and
Chan
,
N. H.
Spatial Modeling of Regional Variables
”.
Journal of the American Statistical Association
,
84
,
393
401
. (
1989
).
13.
Richardson
,
S.
,
Guihenneuc
,
C.
, and
Lasserre
,
V.
Spatial Linear Models with Autocorrelated Error Structure
”.
The Statistician
,
41
,
539
557
. (
1992
).
14.
Bell
,
B. S.
, and
Broemeling
,
L. D.
A Bayesian Analysis of Spatial Processes with Application to Disease Mapping
”.
Statistics in Medicine
,
19
,
957
974
. (
2000
).
15.
Militino
,
A. F.
,
Ugarte
,
M. D.
, and
Garcia-Reinaldos
,
L.
Alternative Models for Describing Spatial Dependence Among Dwelling Selling Prices
”.
Journal of Real Estate Finance and Economics
,
29
,
193
209
. (
2004
).
16.
Clayton
,
D.
, and
Kaldor
,
J.
Empirical Bayes Estimates of Age-Standardized Relative Risks For Use in Disease Mapping
”.
Biometrics
,
43
,
671
681
. (
1987
).
17.
Pettitt
,
A. N.
,
Weir
,
I. S.
, and
Hart
,
A. G.
A Conditional Autoregressive Gaussian Process for Irregularly Spaced Multivariate Data with Application to Modelling Large Sets of Binary Data
”.
Statistics and Computing
,
12
,
353
367
. (
2002
).
18.
Heinen
,
A.
Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model
”.
Munich Personal RePEc Archive
.
8113
. (
2003
).
19.
Diggle
P. J.
,
Rowlingson
B.
, and
Su
T. L.
Point Process Methodology for On-line Spatio-temporal Disease Surveillance
”.
Environmetrics
16
(
5
):
423
434
. (
2005
).
20.
McCulloch
C.
,
Searle
S.
, and
Neuhaus
J.
Generalized, Linear and Mixed Models.
Wiley; New York
. (
2008
)
21.
Leroux
B. G.
,
Lei
X.
, and
Breslow
N.
Statistical Models in Epidemiology, the Environment, and Clinical Trials, chapter Estimation of Disease Rates in Small Areas: A new Mixed Model for Spatial Dependence
”.
Springer-Verlag.
179
191
. (
2000
).
This content is only available via PDF.
You do not currently have access to this content.