Open AccessA simulation study with log, Box-Cox, and dual-power transformation on handling curvilinear relationship in small area estimation
Author(s) -
D. K. Bodro,
Bagus Sartono,
Kusman Sadik
Publication year - 2019
Publication title -
iop conference series. earth and environmental science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.179
H-Index - 26
eISSN - 1755-1307
pISSN - 1755-1315
DOI - 10.1088/1755-1315/299/1/012029
Subject(s) - transformation (genetics) , power transform , mathematics , range (aeronautics) , monotonic function , logarithm , normality , statistics , data transformation , curvilinear coordinates , dual (grammatical number) , function (biology) , computer science , data mining , discrete mathematics , consistency (knowledge bases) , mathematical analysis , art , biochemistry , chemistry , materials science , geometry , literature , evolutionary biology , biology , composite material , data warehouse , gene
A standard small area estimation method may fail to produce reasonable estimates when the normality assumption is not met or the relationship between the interest parameter and the auxiliary variables is not linear. A logarithm transformation has been widely used to help this issue and works well for some cases. However, it may not be generally valid so that some transformation such as Box-Cox (BC) and dual power (DP). This paper discusses a simulation study on how BC and DP could overcome circumstances where those aforementioned problems are there in the data. Several different forms of the relationship were studied and the study revealed that BC and DP transformation are the recommended methods because they produced smaller Mean Absolute Percentage Error (MAPE) values than ones without transformation or using logarithm transformation. Even if DP does not consistently provide the lowest value, but technically, DP can overcome truncated problems that occur in BC. The findings of this work indicate that this new transformation, DP, is proposed to be the best transformation to overcome the abnormality of an interesting variable because this transformation produces a monotonic function that has a domain of positive real numbers (ℝ + ) and range of whole real numbers (ℝ).