Asymptotically Distribution-free Research Articles

MULTIDIMENSIONAL POVERTY MODELING IN CENTRAL JAVA, DI YOGYAKARTA, AND EAST JAVA PROVINCES

Indonesia has a National Medium-Term Development Plan (RPJMN) for 2020-2024 to reduce the poverty rate to 6 to 7 percent. However, the poverty rate has only declined by less than one percent in the past year, indicating the need for optimization to achieve the goal. Despite being located in Java, the center of development and economy in Indonesia, the poverty rate in Central Java, DI Yogyakarta, and East Java still exceeds the national average. This study used SUSENAS 2023 March KOR data to address this challenge and examine the multidimensional indicators affecting poverty. The Alkire-Foster method was used to obtain the Multidimensional Poverty Index (MPI) number, which was then analyzed using the Structural Equation Model (SEM) with the Asymptotically Distribution-free (AD-f) method approach. SEM is used to observe latent variables that cannot be measured and the relationship between variables that form a multidimensional poverty index. AD-f method approach is used to overcome data non-normality in SEM processing. The study revealed that the percentage of multidimensional poverty in the three provinces is higher than monetary poverty due to the household unit of analysis used. The standard of living dimension was the most deprived in most households, followed by the health dimension. To tackle this issue, the study recommends optimizing access to the Internet, assets, preschool participation, and nutrition.

Imperfect repair models: Sequential goodness‐of‐fit testing based on predictive performances

AbstractImperfect repair (IR) modelling has attracted a lot of attention during the last decades. To assess and predict repairable systems' reliability, analysts have to choose among a plethora of models: renewal processes, non‐homogeneous Poisson processes (NHPPs), Brown–Proschan, Kijima, ARA, ARI, Quasi‐Renewal (QR), Trend‐Renewal and so forth. Choosing an appropriate model for a given failures, dataset is an important practical issue. The fit of an IR model can be assessed using goodness‐of‐fit (GoF) tests but very few have been proposed and a good fit to past data does not guarantee good reliability predictions. This work proposes general GoF tests for IR models based on sequential (or on‐line) assessment of times‐to‐failures forecasts. The suggested predictive‐sequential (or prequential) GoF tests have a low computational complexity and a common test statistic for several IR models. These tests have been proved to be asymptotically distribution‐free (ADF) for renewal and power‐law processes (PLPs). Our numerical simulations and preliminary theoretical results highly suggest that this ADF property still holds for several other IR models. The prequential tests are much easier to use than the already known bootstrap tests, and a simulation study shows that they are also slightly more powerful. The simulations also show that the prequential tests are powerful to identify classes of similar appropriate models but are much less powerful to distinguish models belonging to the same class. A comparison of MTTF estimates show that models from the same class give close reliability predictions and that the tests are able to reject models which would yield to dramatic errors in reliability predictions.

Evaluation of the Psychometric Properties of the Arab Compulsive Internet Use Scale (CIUS) by Item Response Theory Modeling (IRT).

Introduction: The psychometric properties of the Arab translation of the Compulsive Internet Use Scale (CIUS) have been previously studied by confirmatory factor analysis (CFA) with AMOS software using the asymptotically distribution-free (ADF) estimator. Unidimensionality has been achieved at the cost of correlating several item variance errors. However, several reviews of SEM software packages and estimation methods indicate that the option of robust standard errors is not present in the AMOS package and that ADF estimation may yield biased parameter estimates. We therefore explored a second analysis through item response theory (IRT) using the parametric graded response model (GRM) and the marginal maximum likelihood (MML) estimation method embedded in the LTM package of R software. Differential item functioning (DIF) or item bias across subpopulations was also explored within IRT framework as different samples were investigated. The objective of the current study is to (1) analyze the Arab CIUS scale with IRT, (2) investigate DIF in three samples, and (3) contribute to the ongoing debate on Internet-use-related addictive behaviors using the CIUS items as a proxy. Methods: We assessed three samples of people, one in Algeria and two in Lebanon, with a total of 1520 participants. Results: Almost three out of every five items were highly related to the latent construct. However, the unidimensionality hypothesis was not supported. Furthermore, besides being locally dependent, the scale may be weakened by DIF across geographic regions. Some of the CIUS items related to increasing priority, impaired control, continued use despite harm, and functional impairment as well as withdrawal and coping showed good discriminative capabilities. Those items were endorsed more frequently than other CIUS items in people with higher levels of addictive Internet use. Conclusions: Contrary to earlier ADF estimation findings, unidimensionality of the CIUS scale was not supported by IRT parametric GRM in a large sample of Arab speaking participants. The results may be helpful for scale revision. By proxy, the study contributes to testing the validity of addiction criteria applied to Internet use related-addictive behaviors.

Distributionally weighted least squares in structural equation modeling.

n real data analysis with structural equation modeling, data are unlikely to be exactly normally distributed. If we ignore the non-normality reality, the parameter estimates, standard error estimates, and model fit statistics from normal theory based methods such as maximum likelihood (ML) and normal theory based generalized least squares estimation (GLS) are unreliable. On the other hand, the asymptotically distribution free (ADF) estimator does not rely on any distribution assumption but cannot demonstrate its efficiency advantage with small and modest sample sizes. The methods which adopt misspecified loss functions including ridge GLS (RGLS) can provide better estimates and inferences than the normal theory based methods and the ADF estimator in some cases. We propose a distributionally weighted least squares (DLS) estimator, and expect that it can perform better than the existing generalized least squares, because it combines normal theory based and ADF based generalized least squares estimation. Computer simulation results suggest that model-implied covariance based DLS (DLSM) provided relatively accurate and efficient estimates in terms of RMSE. In addition, the empirical standard errors, the relative biases of standard error estimates, and the Type I error rates of the Jiang-Yuan rank adjusted model fit test statistic (TJY) in DLSM were competitive with the classical methods including ML, GLS, and RGLS. The performance of DLSM depends on its tuning parameter a. We illustrate how to implement DLSM and select the optimal a by a bootstrap procedure in a real data example. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Distributionally-Weighted Least Squares in Growth Curve Modeling

ABSTRACT Growth curve modeling is commonly used in psychological, educational, and social science research. The mainstream estimators for growth curve modeling are based on normal theory, but real data are unlikely to be exactly normally distributed. To improve estimation and inference with non-normal data, various estimators have been proposed. Among these estimators, the asymptotically distribution free (ADF) estimator does not need to rely on any distribution assumption but it is not efficient with small and modest sample sizes. We propose a distributionally weighted least squares estimator in the growth curve modeling framework. combines normal theory based and based generalized least squares estimation to balance the information from the data and the normality assumption. Computer simulation results suggest that model-implied covariance-based () generally provides more accurate and efficient estimates than the examined alternative methods regardless of the distribution. In addition, the relative biases of standard error estimates and the Type I error rates of the Satorra–Bentler test statistic () in were competitive with the classical methods including maximum likelihood and generalized least squares estimation. We illustrate how to implement and select the optimal tuning parameter by a bootstrap procedure in a real data example.

The Effects of Surprises Factors Macroeconomic to Earnings Surprises and Market Liquidity and Impact to Stock Return.

This paper approach a Structural Equation Model design by method Asymptotically Distribution Free (ADF) to analyzed the surprises factors macroeconomic affect the stock return with both market liquidity and earnings surprises. The monthly financial sector data with 59 firms’ for the years 2012-2016 and using the purposive sampling method. The result indicated that’s surprises factors macroeconomic is significant to earnings surprises and stock returns also earnings surprises to returns but not to market liquidity and liquidity to stock returns.

Examining the Performance of the Modified ADF Goodness-of-fit Test Statistic in Structural Equation Models

The asymptotically distribution-free (ADF) test statistic depends on very mild distributional assumptions and is theoretically superior to many other so-called robust tests available in structural equation modeling. The ADF test, however, often leads to model overrejection even at modest sample sizes. To overcome its poor small-sample performance, a family of robust test statistics obtained by modifying the ADF statistics was recently proposed. This study investigates by simulation the performance of the new modified test statistics. The results revealed that although a few of the test statistics adequately controlled Type I error rates in each of the examined conditions, most performed quite poorly. This result underscores the importance of choosing a modified test statistic that performs well for specific examined conditions. A parametric bootstrap method is proposed for identifying such a best-performing modified test statistic. Through further simulation it is shown that the proposed bootstrap approach performs well.

Asymptotic distribution-free tests for semiparametric regressions with dependent data

This article proposes a new general methodology for constructing nonparametric and semiparametric Asymptotically Distribution-Free (ADF) tests for semiparametric hypotheses in regression models for possibly dependent data coming from a strictly stationary process. Classical tests based on the difference between the estimated distributions of the restricted and unrestricted regression errors are not ADF. In this article, we introduce a novel transformation of this difference that leads to ADF tests with well-known critical values. The general methodology is illustrated with applications to testing for parametric models against nonparametric or semiparametric alternatives, and semiparametric constrained mean–variance models. Several Monte Carlo studies and an empirical application show that the finite sample performance of the proposed tests is satisfactory in moderate sample sizes.

Resampling-Based Inference Methods for Comparing Two Coefficients Alpha.

The two-sample problem for Cronbach's coefficient [Formula: see text], as an estimate of test or composite score reliability, has attracted little attention compared to the extensive treatment of the one-sample case. It is necessary to compare the reliability of a test for different subgroups, for different tests or the short and long forms of a test. In this paper, we study statistical procedures of comparing two coefficients [Formula: see text] and [Formula: see text]. The null hypothesis of interest is [Formula: see text], which we test against one-or two-sided alternatives. For this purpose, resampling-based permutation and bootstrap tests are proposed for two-group multivariate non-normal models under the general asymptotically distribution-free (ADF) setting. These statistical tests ensure a better control of the type-I error, in finite or very small sample sizes, when the state-of-affairs ADF large-sample test may fail to properly attain the nominal significance level. By proper choice of a studentized test statistic, the resampling tests are modified in order to be valid asymptotically even in non-exchangeable data frameworks. Moreover, extensions of this approach to other designs and reliability measures are discussed as well. Finally, the usefulness of the proposed resampling-based testing strategies is demonstrated in an extensive simulation study and illustrated by real data applications.

Modified Distribution-Free Goodness-of-Fit Test Statistic.

Covariance structure analysis and its structural equation modeling extensions have become one of the most widely used methodologies in social sciences such as psychology, education, and economics. An important issue in such analysis is to assess the goodness of fit of a model under analysis. One of the most popular test statistics used in covariance structure analysis is the asymptotically distribution-free (ADF) test statistic introduced by Browne (Br J Math Stat Psychol 37:62-83, 1984). The ADF statistic can be used to test models without any specific distribution assumption (e.g., multivariate normal distribution) of the observed data. Despite its advantage, it has been shown in various empirical studies that unless sample sizes are extremely large, this ADF statistic could perform very poorly in practice. In this paper, we provide a theoretical explanation for this phenomenon and further propose a modified test statistic that improves the performance in samples of realistic size. The proposed statistic deals with the possible ill-conditioning of the involved large-scale covariance matrices.

Modified Distribution-Free Goodness of Fit Test Statistic

Covariance structure analysis and its structural equation modeling extensions have become one of the most widely used methodologies in social sciences such as psychology, education, and economics. An important issue in such analysis is to assess the goodness-of-fit of a model under analysis. One of the most popular test statistics is the asymptotically distribution free (ADF) test statistic introduced by Browne in 1984. The ADF statistic can be used to test models without any specific distribution assumption (e.g., multivariate normal distribution) of the observed data. Despite its advantage, it has been shown in various empirical studies that unless sample sizes are extremely large, this ADF statistic can perform very poorly in practice. In this paper, we provide a theoretical explanation for this phenomenon and further propose a modified test statistic that improves the performance in samples of realistic size. The proposed statistic deals with the possible ill conditioning of the involved large scale covariance matrices.

Behavior of Asymptotically Distribution Free Test Statistics in Covariance Versus Correlation Structure Analysis

The asymptotically distribution free (ADF) method is often used to estimate parameters or test models without a normal distribution assumption on variables, both in covariance structure analysis and in correlation structure analysis. However, little has been done to study the differences in behaviors of the ADF method in covariance versus correlation structure analysis. The behaviors of 3 test statistics frequently used to evaluate structural equation models with nonnormally distributed variables, χ2 test TAGLS and its small-sample variants TYB and TF(AGLS) were compared. Results showed that the ADF method in correlation structure analysis with test statistic TAGLS performs much better at small sample sizes than the corresponding test for covariance structures. In contrast, test statistics TYB and TF(AGLS) under the same conditions generally perform better with covariance structures than with correlation structures. It is proposed that excessively large and variable condition numbers of weight matrices are a cause of poor behavior of ADF test statistics in small samples, and results showed that these condition numbers are systematically increased with substantial increase in variance as sample size decreases. Implications for research and practice are discussed.

Improvement of the quality of the chi-square approximation for the ADF test on a covariance matrix with a linear structure

The asymptotically distribution-free (ADF) test statistic was proposed by Browne (1984). It is known that the null distribution of the ADF test statistic is asymptotically distributed according to the chi-square distribution. This asymptotic property is always satisfied, even under nonnormality, although the null distributions of other famous test statistics, e.g., the maximum likelihood test statistic and the generalized least square test statistic, do not converge to the chi-square distribution under nonnormality. However, many authors have reported numerical results which indicate that the quality of the chi-square approximation for the ADF test is very poor, even when the sample size is large and the population distribution is normal. In this paper, we try to improve the quality of the chi-square approximation to the ADF test for a covariance matrix with a linear structure by using the Bartlett correction applicable under the assumption of normality. By conducting numerical studies, we verify that the obtained Bartlett correction can perform well even when the assumption of normality is violated.

Asymptotically Distribution-Free Goodness-of-Fit Testing: A Unifying View

We outline a general paradigm for constructing asymptotically distribution-free (ADF) goodness-of-fit tests, which can be regarded as a generalization of Khmaladze (1993). This is achieved by a nonorthogonal projection of a class of functions onto the ortho-complement of the extended tangent space (ETS) associated with the null hypothesis. In parallel with the work of Bickel et al. (2006), we obtain transformed empirical processes (TEP) which are the building blocks for constructing omnibus tests such as the usual Kolmogorov–Smirnov type tests and Crámer–von Mise type tests, as well as Portmanteau tests and directional tests. The critical values can be tabulated due to the ADF property. All the tests are capable of detecting local (Pitman) alternative at the root-n scale. We shall illustrate the framework in several examples, mostly in regression model specification testing.

Testing Reliability Hypotheses Based on Coefficient Alpha

We show how to test hypotheses for coefficient alpha in three different situations: (1) Hypothesis tests of whether coefficient alpha equals a prespecified value. (2) Hypothesis tests involving two statistically independent sample alphas as may arise when testing the equality of coefficient alpha across groups. (3) Hypothesis tests involving two statistically dependent sample alphas as may arise when testing the equality of alpha across time, or when testing the equality of alpha for two test scores within the same sample. We illustrate how these hypotheses may be tested in a structural equation modeling framework under the assumption of normally distributed responses and also under asymptotically distribution free (ADF) assumptions. The formulas for the hypothesis tests and computer code are given for four different applied examples.

Asymptotic Distribution Free Interval Estimation

Abstract. Confidence intervals for the intraclass correlation coefficient (ICC) have been proposed under the assumption of multivariate normality. We propose confidence intervals which do not require distributional assumptions. We performed a simulation study to assess the coverage rates of normal theory (NT) and asymptotically distribution free (ADF) intervals. We found that the ADF intervals performed better than the NT intervals when kurtosis was greater than 4. When violations of distributional assumptions were not too severe, both the intervals performed about the same. The point estimate of the ICC was robust to distributional violations. We provide R code for computing the ADF confidence intervals for the ICC.

Asymptotically distribution-free (ADF) interval estimation of coefficient alpha.

The point estimate of sample coefficient alpha may provide a misleading impression of the reliability of the test score. Because sample coefficient alpha is consistently biased downward, it is more likely to yield a misleading impression of poor reliability. The magnitude of the bias is greatest precisely when the variability of sample alpha is greatest (small population reliability and small sample size). Taking into account the variability of sample alpha with an interval estimator may lead to retaining reliable tests that would be otherwise rejected. Here, the authors performed simulation studies to investigate the behavior of asymptotically distribution-free (ADF) versus normal-theory interval estimators of coefficient alpha under varied conditions. Normal-theory intervals were found to be less accurate when item skewness >1 or excess kurtosis >1. For sample sizes over 100 observations, ADF intervals are preferable, regardless of item skewness and kurtosis. A formula for computing ADF confidence intervals for coefficient alpha for tests of any size is provided, along with its implementation as an SAS macro.

"Asymptotically distribution-free (ADF) interval estimation of coefficient alpha": Correction.

"Asymptotically distribution-free (ADF) interval estimation of coefficient alpha": Correction.

A Statistically Justified Pairwise ML Method for Incomplete Nonnormal Data: A Comparison With Direct ML and Pairwise ADF

This article proposes a new approach to the statistical analysis of pairwise-present covariance structure data. The estimator is based on maximizing the complete data likelihood function, and the associated test statistic and standard errors are corrected for misspecification using Satorra-Bentler corrections. A Monte Carlo study was conducted to compare the proposed method (pairwise maximum likelihood [ML]) to 2 other methods for dealing with incomplete nonnormal data: direct ML estimation with the Yuan-Bentler corrections for nonnormality (direct ML) and the asymptotically distribution free (ADF) method applied to available cases (pairwise ADF). Data were generated from a 4-factor model with 4 indicators per factor; sample size varied from 200 to 5,000; data were either missing completely at random (MCAR) or missing at random (MAR); and the proportion of missingness was either 15% or 30%. Measures of relative performance included model fit, relative accuracy in parameter estimates and their standard errors, and efficiency of parameter estimates. The results generally favored direct ML over either of the pairwise methods, except at N = 5,000, when ADF outperformed both ML methods with MAR data. The inferior performance of the 2 pairwise methods was primarily due to inflated test statistics. Among the unexpected findings was that ADF did better at estimating factor covariances in all conditions, and that MCAR data presented more problems for all methods than did MAR data, in terms of convergence, performance of test statistics, and relative accuracy of parameter estimates.

Dimensionality of the Maslach Burnout Inventory in School Teachers

Abstract. The Maslach Burnout Inventory (MBI) is an instrument which has been used worldwide to assess occupational stress in human service professions. While the MBI has been used in school settings, an inventory specifically oriented to measure burnout in teachers was developed (MBI-Form Ed; Schwab, in Maslach & Jackson, 1986 ). A Catalan version of the MBI-Form Ed was administered to 631 elementary school teachers. Several models, including those posited by some studies using the English language MBI-Form Ed, were analyzed in order to test their cross-cultural validity. Confirmatory factor analyses (CFAs) were used to fit all models by maximum likelihood (ML) and asymptotically distribution-free (ADF) estimation methods to test the hypothesis that incorrect use of the ML estimation method could be the reason for model misfit in previous studies. Results show that there are no differences due to the estimation method and support the three-factor structure. Furthermore, a shortened three-factor model of 17 items shows a better fit and similar reliability, and its use seems plausible in the research and psychological evaluation of teachers' burnout in both English and Catalan language settings.