scholarly journals A Machine Learning Approach to Assess Differential Item Functioning in Psychometric Questionnaires Using the Elastic Net Regularized Ordinal Logistic Regression in Small Sample Size Groups

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Vahid Ebrahimi ◽  
Zahra Bagheri ◽  
Zahra Shayan ◽  
Peyman Jafari
Keyword(s):  
Sample Size ◽  
Type I Error ◽  
Small Sample Size ◽  
Error Rates ◽  
Small Sample ◽  
Elastic Net ◽  
Small Samples ◽  
Type I ◽  
Item Functioning ◽  
Size Groups

Assessing differential item functioning (DIF) using the ordinal logistic regression (OLR) model highly depends on the asymptotic sampling distribution of the maximum likelihood (ML) estimators. The ML estimation method, which is often used to estimate the parameters of the OLR model for DIF detection, may be substantially biased with small samples. This study is aimed at proposing a new application of the elastic net regularized OLR model, as a special type of machine learning method, for assessing DIF between two groups with small samples. Accordingly, a simulation study was conducted to compare the powers and type I error rates of the regularized and nonregularized OLR models in detecting DIF under various conditions including moderate and severe magnitudes of DIF ( DIF = 0.4   and   0.8 ), sample size ( N ), sample size ratio ( R ), scale length ( I ), and weighting parameter ( w ). The simulation results revealed that for I = 5 and regardless of R , the elastic net regularized OLR model with w = 0.1 , as compared with the nonregularized OLR model, increased the power of detecting moderate uniform DIF ( DIF = 0.4 ) approximately 35% and 21% for N = 100   and   150 , respectively. Moreover, for I = 10 and severe uniform DIF ( DIF = 0.8 ), the average power of the elastic net regularized OLR model with 0.03 ≤ w ≤ 0.06 , as compared with the nonregularized OLR model, increased approximately 29.3% and 11.2% for N = 100   and   150 , respectively. In these cases, the type I error rates of the regularized and nonregularized OLR models were below or close to the nominal level of 0.05. In general, this simulation study showed that the elastic net regularized OLR model outperformed the nonregularized OLR model especially in extremely small sample size groups. Furthermore, the present research provided a guideline and some recommendations for researchers who conduct DIF studies with small sample sizes.

scholarly journals Taking population stratification into account by local permutations in rare-variant association studies on small samples

2020 ◽  
Author(s):  
J. Mullaert ◽  
M. Bouaziz ◽  
Y. Seeleuthner ◽  
B. Bigio ◽  
J-L. Casanova ◽  
...  
Keyword(s):  
Sample Size ◽  
Rare Variant ◽  
Population Stratification ◽  
Type I Error ◽  
Small Sample Size ◽  
Association Studies ◽  
Small Sample ◽  
Small Samples ◽  
Type I ◽  
Rare Variant Association

AbstractMany methods for rare variant association studies require permutations to assess the significance of tests. Standard permutations assume that all individuals are exchangeable and do not take population stratification (PS), a known confounding factor in genetic studies, into account. We propose a novel strategy, LocPerm, in which individuals are permuted only with their closest ancestry-based neighbors. We performed a simulation study, focusing on small samples, to evaluate and compare LocPerm with standard permutations and classical adjustment on first principal components. Under the null hypothesis, LocPerm was the only method providing an acceptable type I error, regardless of sample size and level of stratification. The power of LocPerm was similar to that of standard permutation in the absence of PS, and remained stable in different PS scenarios. We conclude that LocPerm is a method of choice for taking PS and/or small sample size into account in rare variant association studies.

scholarly journals Assessment of Type I Error Rates and Power of Common Analysis Methods in Murine Obesity-Related Study: ‘Plasmode-Based’ Simulation (P13-011-19)

2019 ◽  
Vol 3 (Supplement_1) ◽  
Author(s):  
Keisuke Ejima ◽  
Andrew Brown ◽  
Daniel Smith ◽  
Ufuk Beyaztas ◽  
David Allison
Keyword(s):  
Sample Size ◽  
Error Rate ◽  
Type I Error ◽  
Error Rates ◽  
T Test ◽  
Small Samples ◽  
Type I ◽  
Type I Error Rates ◽  
Type I Error Rate ◽  
Weight Distributions

Abstract Objectives Rigor, reproducibility and transparency (RRT) awareness has expanded over the last decade. Although RRT can be improved from various aspects, we focused on type I error rates and power of commonly used statistical analyses testing mean differences of two groups, using small (n ≤ 5) to moderate sample sizes. Methods We compared data from five distinct, homozygous, monogenic, murine models of obesity with non-mutant controls of both sexes. Baseline weight (7–11 weeks old) was the outcome. To examine whether type I error rate could be affected by choice of statistical tests, we adjusted the empirical distributions of weights to ensure the null hypothesis (i.e., no mean difference) in two ways: Case 1) center both weight distributions on the same mean weight; Case 2) combine data from control and mutant groups into one distribution. From these cases, 3 to 20 mice were resampled to create a ‘plasmode’ dataset. We performed five common tests (Student's t-test, Welch's t-test, Wilcoxon test, permutation test and bootstrap test) on the plasmodes and computed type I error rates. Power was assessed using plasmodes, where the distribution of the control group was shifted by adding a constant value as in Case 1, but to realize nominal effect sizes. Results Type I error rates were unreasonably higher than the nominal significance level (type I error rate inflation) for Student's t-test, Welch's t-test and permutation especially when sample size was small for Case 1, whereas inflation was observed only for permutation for Case 2. Deflation was noted for bootstrap with small sample. Increasing sample size mitigated inflation and deflation, except for Wilcoxon in Case 1 because heterogeneity of weight distributions between groups violated assumptions for the purposes of testing mean differences. For power, a departure from the reference value was observed with small samples. Compared with the other tests, bootstrap was underpowered with small samples as a tradeoff for maintaining type I error rates. Conclusions With small samples (n ≤ 5), bootstrap avoided type I error rate inflation, but often at the cost of lower power. To avoid type I error rate inflation for other tests, sample size should be increased. Wilcoxon should be avoided because of heterogeneity of weight distributions between mutant and control mice. Funding Sources This study was supported in part by NIH and Japan Society for Promotion of Science (JSPS) KAKENHI grant.

scholarly journals Differences of Type I error rates for ANOVA and Multilevel-Linear-Models using SAS and SPSS for repeated measures designs

2019 ◽  
Vol 3 ◽  
Author(s):  
Nicolas Haverkamp ◽  
André Beauducel
Keyword(s):  
Repeated Measures ◽  
Linear Models ◽  
Type I Error ◽  
Error Rates ◽  
Small Sample ◽  
Small Samples ◽  
Type I ◽  
Sample Sizes ◽  
Type I Error Rates ◽  
Multilevel Linear Models

  To derive recommendations on how to analyze longitudinal data, we examined Type I error rates of Multilevel Linear Models (MLM) and repeated measures Analysis of Variance (rANOVA) using SAS and SPSS. We performed a simulation with the following specifications: To explore the effects of high numbers of measurement occasions and small sample sizes on Type I error, measurement occasions of m = 9 and 12 were investigated as well as sample sizes of n = 15, 20, 25 and 30. Effects of non-sphericity in the population on Type I error were also inspected: 5,000 random samples were drawn from two populations containing neither a within-subject nor a between-group effect. They were analyzed including the most common options to correct rANOVA and MLM-results: The Huynh-Feldt-correction for rANOVA (rANOVA-HF) and the Kenward-Roger-correction for MLM (MLM-KR), which could help to correct progressive bias of MLM with an unstructured covariance matrix (MLM-UN). Moreover, uncorrected rANOVA and MLM assuming a compound symmetry covariance structure (MLM-CS) were also taken into account. The results showed a progressive bias for MLM-UN for small samples which was stronger in SPSS than in SAS. Moreover, an appropriate bias correction for Type I error via rANOVA-HF and an insufficient correction by MLM-UN-KR for n < 30 were found. These findings suggest MLM-CS or rANOVA if sphericity holds and a correction of a violation via rANOVA-HF. If an analysis requires MLM, SPSS yields more accurate Type I error rates for MLM-CS and SAS yields more accurate Type I error rates for MLM-UN.

A Monte Carlo Comparison of Seven ε-Adjustment Procedures in Repeated Measures Designs With Small Sample Sizes

1994 ◽  
Vol 19 (1) ◽  
pp. 57-71 ◽  
Author(s):  
Stephen M. Quintana ◽  
Scott E. Maxwell
Keyword(s):  
Repeated Measures ◽  
Type I Error ◽  
Error Rates ◽  
Small Sample ◽  
Small Samples ◽  
Type I ◽  
Sample Sizes ◽  
Type I Error Rates ◽  
Repeated Measures Designs ◽  
Small Sample Sizes

The purpose of this study was to evaluate seven univariate procedures for testing omnibus null hypotheses for data gathered from repeated measures designs. Five alternate approaches are compared to the two more traditional adjustment procedures (Geisser and Greenhouse’s ε̂ and Huynh and Feldt’s ε̃), neither of which may be entirely adequate when sample sizes are small and the number of levels of the repeated factors is large. Empirical Type I error rates and power levels were obtained by simulation for conditions where small samples occur in combination with many levels of the repeated factor. Results suggested that alternate univariate approaches were improvements to the traditional approaches. One alternate approach in particular was found to be most effective in controlling Type I error rates without unduly sacrificing power.

SMALL SAMPLE SIZE SCIENTIST

PEDIATRICS ◽  
1989 ◽  
Vol 83 (3) ◽  
pp. A72-A72
Author(s):  
Student
Keyword(s):  
Sample Size ◽  
Confidence Intervals ◽  
Causal Explanation ◽  
Small Sample Size ◽  
Small Sample ◽  
Small Samples ◽  
High Expectations ◽  
Sampling Variation ◽  
The Law ◽  
The Stability

The believer in the law of small numbers practices science as follows: 1. He gambles his research hypotheses on small samples without realizing that the odds against him are unreasonably high. He overestimates power. 2. He has undue confidence in early trends (e.g., the data of the first few subjects) and in the stability of observed patterns (e.g., the number and identity of significant results). He overestimates significance. 3. In evaluating replications, his or others', he has unreasonably high expectations about the replicability of significant results. He underestimates the breadth of confidence intervals. 4. He rarely attributes a deviation of results from expectations to sampling variability, because he finds a causal "explanation" for any discrepancy. Thus, he has little opportunity to recognize sampling variation in action. His belief in the law of small numbers, therefore, will forever remain intact.

scholarly journals Cluster Wild Bootstrapping to Handle Dependent Effect Sizes in Meta-Analysis with a Small Number of Studies

2021 ◽  
Author(s):  
Megha Joshi ◽  
James E Pustejovsky ◽  
S. Natasha Beretvas
Keyword(s):  
Effect Size ◽  
Type I Error ◽  
Meta Analysis ◽  
Error Rates ◽  
Small Sample ◽  
Type I ◽  
Hypothesis Tests ◽  
Type I Error Rates ◽  
Meta Analyses ◽  
Small Sample Correction

The most common and well-known meta-regression models work under the assumption that there is only one effect size estimate per study and that the estimates are independent. However, meta-analytic reviews of social science research often include multiple effect size estimates per primary study, leading to dependence in the estimates. Some meta-analyses also include multiple studies conducted by the same lab or investigator, creating another potential source of dependence. An increasingly popular method to handle dependence is robust variance estimation (RVE), but this method can result in inflated Type I error rates when the number of studies is small. Small-sample correction methods for RVE have been shown to control Type I error rates adequately but may be overly conservative, especially for tests of multiple-contrast hypotheses. We evaluated an alternative method for handling dependence, cluster wild bootstrapping, which has been examined in the econometrics literature but not in the context of meta-analysis. Results from two simulation studies indicate that cluster wild bootstrapping maintains adequate Type I error rates and provides more power than extant small sample correction methods, particularly for multiple-contrast hypothesis tests. We recommend using cluster wild bootstrapping to conduct hypothesis tests for meta-analyses with a small number of studies. We have also created an R package that implements such tests.

scholarly journals Detecting Differential Item Functioning Using Multiple-Group Cognitive Diagnosis Models

2020 ◽  
Vol 45 (1) ◽  
pp. 37-53
Author(s):  
Wenchao Ma ◽  
Ragip Terzi ◽  
Jimmy de la Torre
Keyword(s):  
Differential Item Functioning ◽  
Type I Error ◽  
Search Algorithm ◽  
Real Data ◽  
Error Rates ◽  
Cognitive Diagnosis ◽  
Type I ◽  
Wald Tests ◽  
Multiple Group ◽  
Item Functioning

This study proposes a multiple-group cognitive diagnosis model to account for the fact that students in different groups may use distinct attributes or use the same attributes but in different manners (e.g., conjunctive, disjunctive, and compensatory) to solve problems. Based on the proposed model, this study systematically investigates the performance of the likelihood ratio (LR) test and Wald test in detecting differential item functioning (DIF). A forward anchor item search procedure was also proposed to identify a set of anchor items with invariant item parameters across groups. Results showed that the LR and Wald tests with the forward anchor item search algorithm produced better calibrated Type I error rates than the ordinary LR and Wald tests, especially when items were of low quality. A set of real data were also analyzed to illustrate the use of these DIF detection procedures.

scholarly journals Improved Small Sample Inference Methods for a Mixed-Effects Model for Repeated Measures Approach in Incomplete Longitudinal Data Analysis

Stats ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 174-188
Author(s):  
Yoshifumi Ukyo ◽  
Hisashi Noma ◽  
Kazushi Maruo ◽  
Masahiko Gosho
Keyword(s):  
Clinical Trial ◽  
Repeated Measures ◽  
Type I Error ◽  
Mixed Effects ◽  
Error Rates ◽  
Small Sample ◽  
Mixed Effects Model ◽  
Model Complexity ◽  
Type I ◽  
Inference Methods

The mixed-effects model for repeated measures (MMRM) approach has been widely applied for longitudinal clinical trials. Many of the standard inference methods of MMRM could possibly lead to the inflation of type I error rates for the tests of treatment effect, when the longitudinal dataset is small and involves missing measurements. We propose two improved inference methods for the MMRM analyses, (1) the Bartlett correction with the adjustment term approximated by bootstrap, and (2) the Monte Carlo test using an estimated null distribution by bootstrap. These methods can be implemented regardless of model complexity and missing patterns via a unified computational framework. Through simulation studies, the proposed methods maintain the type I error rate properly, even for small and incomplete longitudinal clinical trial settings. Applications to a postnatal depression clinical trial are also presented.

Comparison of a Two-Stage and Three-Stage Interim-Analysis Procedure

1992 ◽  
Vol 71 (1) ◽  
pp. 3-14 ◽  
Author(s):  
John E. Overall ◽  
Robert S. Atlas
Keyword(s):  
Sample Size ◽  
Interim Analysis ◽  
Type I Error ◽  
Substantial Reduction ◽  
Error Rates ◽  
Sampling Plan ◽  
Type I ◽  
Two Stage ◽  
Expected Sample Size ◽  
Analysis Strategy

A statistical model for combining p values from multiple tests of significance is used to define rejection and acceptance regions for two-stage and three-stage sampling plans. Type I error rates, power, frequencies of early termination decisions, and expected sample sizes are compared. Both the two-stage and three-stage procedures provide appropriate protection against Type I errors. The two-stage sampling plan with its single interim analysis entails minimal loss in power and provides substantial reduction in expected sample size as compared with a conventional single end-of-study test of significance for which power is in the adequate range. The three-stage sampling plan with its two interim analyses introduces somewhat greater reduction in power, but it compensates with greater reduction in expected sample size. Either interim-analysis strategy is more efficient than a single end-of-study analysis in terms of power per unit of sample size.

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