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Efficiency of Parameter Estimator of Various Resampling Methods on Warppls Analysis Mathematics and Statistics 8(5): 481-492, 2020 http://www.hrpub.org DOI: 10.13189/ms.2020.080501 Efficiency of Parameter Estimator of Various Resampling Methods on WarpPLS Analysis Luthfatul Amaliana, Solimun*, Adji Achmad Rinaldo Fernandes, Nurjannah Department of Statistics, Faculty of Mathematics and Natural Sciences, Brawijaya University, Indonesia Received May 9, 2020; Revised July 16, 2020; Accepted July 29, 2020 Cite This Paper in the following Citation Styles (a): [1] Luthfatul Amaliana, Solimun, Adji Achmad Rinaldo Fernandes, Nurjannah , "Efficiency of Parameter Estimator of Various Resampling Methods on WarpPLS Analysis," Mathematics and Statistics, Vol. 8, No. 5, pp. 481 - 492, 2020. DOI: 10.13189/ms.2020.080501. (b): Luthfatul Amaliana, Solimun, Adji Achmad Rinaldo Fernandes, Nurjannah (2020). Efficiency of Parameter Estimator of Various Resampling Methods on WarpPLS Analysis. Mathematics and Statistics, 8(5), 481 - 492. DOI: 10.13189/ms.2020.080501. Copyright©2020 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abstract WarpPLS analysis has three algorithms, 1. Introduction namely the outer model parameter estimation algorithm, the inner model, and the hypothesis testing algorithm Structural Equation Modeling (SEM) is an analysis to which consists of several choices of resampling methods obtain data and relationships between latent variables that namely Stable1, Stable2, Stable3, Bootstrap, Jackknife, are carried out simultaneously [1]. PLS is a method that is and Blindfolding. The purpose of this study is to apply the more complicated than SEM because it can be applied to WarpPLS analysis by comparing the six resampling the reflective indicator model and the formative indicator methods based on the relative efficiency of the parameter model. The WarpPLS method is the development of Partial estimates in the six methods. This study uses secondary Least Square (PLS) analysis which can identify and predict data from the questionnaire with 1 variable being relationships between linear and non-linear latent variables. formative and 2 variables being reflective. Secondary data WarpPLS analysis has three algorithms: the outer model for the Infrastructure Service Satisfaction Index (IKLI) parameter estimation algorithm, the inner model, and the were obtained from the Study Report on the Regional hypothesis testing algorithm [2]. Development Planning for Economic Growth and the The hypothesis testing algorithm in WarpPLS uses a Malang City Gini Index in 2018, while secondary data for resampling algorithm that consists of various resampling the Social Capital Index (IMS) and Community methods: Stable1, Stable2, Stable3, Bootstrap, Jackknife, Development Index (IPMas) were obtained from the and Blindfolding. Stable1, Stable2, and Stable3 are the Research Report on Performance Indicators Regional latest resampling methods in WarpPLS analysis. This Human Development Index and Poverty Rate of Malang method uses a quasi-parametric approach or method, which is a p-value approximated by the average value. City in 2018. The results of this study indicate that based In the Bootstrap resampling method, the resampling is on two criteria used, namely the calculation of relative done with a certain sample size and repeated by 100 times efficiency and measure of fit as a model good, it can be to achieve convergence. In the Jackknife method, concluded that the Jackknife resampling method is the resampling is done by removing one line and repeating most efficient, followed with the Stable1, Bootstrap, until the last sample. Whereas the Blindfolding method is Stable3, Stable2, and Blindfolding methods. more similar to the Jackknife method, but the first row data Keywords Partial Least Square, Resampling, is replaced by the average of each column (variable) and WarpPLS then continued until the last row. Of the six resampling methods, the most commonly used is the Bootstrap resampling method. 482 Efficiency of Parameter Estimator of Various Resampling Methods on WarpPLS Analysis Based on previous research, the Blindfolding resampling presence of more than one factor contained in a set of method is more efficient than the Bootstrap resampling indicators on a variable. Because formative indicators do method [3]. Other research states that the Stable3 not require common factors, so composite latent variables resampling method which becomes the default setting in will always be obtained [1]. the WarpPLS program package is also more efficient than WarpPLS is a method and software of program package the Bootstrap and Stable2 resampling methods [4]. application developed by Ned Kock [4] to analyze variant Therefore, this study wants to find out which resampling or PLS-based SEM models. It is not only used for method is the most efficient of the six resampling methods non-recursive models but also non-linear model analysis found in the WarpPLS analysis: Stable1, Stable2, Stable3, (Warp2 and Warp3). Bootstrap, Jackknife, and Blindfolding resampling According to [1], the structural model in WarpPLS methods, especially on the data used, namely the consists of two things: Satisfaction Index Infrastructure Services, Social Capital 1) Outer model is the collection of latent variable data Index, and Malang City Community Development Index. sourced from its indicator, consisting of reflective or formative indicator models. 2) Inner models are the relationship model between 2. Materials and Methods recursive and not recursive latent variables. Structural equation modeling or SEM is a technique used to describe the simultaneous relationship of linear relations 2.1. WarpPLS Method between observational variables, which also involves latent WarpPLS analysis has three-parameter estimation variables that cannot be measured directly [2]. SEM algorithms: outer model estimation algorithm, inner model, analysis initially combines a system of simultaneous and hypothesis testing algorithm [2]. The estimation of the equations, path analysis, or regression analysis with factor analysis. Factor analysis is used as a method for obtaining outer model parameter algorithm is the calculation process latent variable data. The process of estimating parameters to produce latent variable data sourced from data items, and testing is based on the concept of a indicators, or dimensions. While the inner model variance-covariance matrix, so it is often referred to as estimation algorithm is the method and process of path covariance-based SEM [1]. coefficient calculation, that is the coefficient of the According to [1], the WarpPLS analysis is a influence of explanatory/predictor variables on the development of the PLS analysis. PLS model was response/dependent variable. In the hypothesis testing developed as an alternative when the model design has a algorithm, WarpPLS analysis uses a resampling algorithm weak or undiscovered theory, or some indicators could not [7]: be measured by reflective measurements so that it was 1) Stable1 is an approach or a method of quasi formative [5]. PLS is a powerful method because it does parametric, and the p-value is approached by the not require a lot of assumptions, and the sample size can be grade point average. small or large. Besides to use as a confirmation of theory 2) Stable 2 produces a consistent guess, through the (hypothesis testing), PLS can also be used to build Bootstrap resampling algorithm. relationships that do not have a theoretical basis or to test 3) Stable 3 produces consistent allegations, through the propositions. Bootstrap resampling algorithm. If the structural model to be analyzed is not recursive, 4) Bootstrap is the resampling with a certain sample size and latent variables have formative, reflective, or mixed (equal or smaller than the original sample) and indicators, one of the appropriate methods to be applied is repeated by 100 times (Bootstrap samples) to achieve PLS [6]. PLS can avoid indeterminacy factor, namely the convergence can see in Figure 1. Mathematics and Statistics 8(5): 481-492, 2020 483 Population (N=135) Original Sample (n=108) Sample Bootstrap B1 Sample Bootstrap B2 Sample Bootstrap B100 (n1=108) (n2=108) (n100=108) Figure 1. Bootstrap Resampling Illustration 5) Jackknife is a method by removing one row (one sample) and being repeated until the last sample. In this method, the sample is reduced by one based on Figure 2. Population (N=135) Original Sample (n=108) Sample Jackknife J1 Sample Jackknife J2 Sample Jackknife J108 (n1=107) (n2=107) (n108=107) Figure 2. Jackknife Resampling Illustration 6) Blindfolding is similar to Jackknife but the first row data is replaced by the average of each column (variable) and continued by the second until the last row [8]. As with the Bootstrap method, it will converge to 100 repetitions following the Figure 3. 484 Efficiency of Parameter Estimator of Various Resampling Methods on WarpPLS Analysis Population (N=135) Original Sample (n=108) Sample Blindfolding F1 Sample Blindfolding F2 Sample Blindfolding F108 (n1=108) (n2=108) (n100=108) Figure 3. Blindfolding Resampling Illustration 2.2. Hypothesis Testing (Resampling) Description: : path coefficient of the influence of endogenous Hypothesis testing in the WarpPLS analysis is done by the resampling method. It guarantees data to be variables on the endogenous variable distribution-free. This study uses six types of resampling: : the influence of exogenous variables on the Stable1,
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