scholarly journals 3-Step ML Auxiliary Variable Integration Using MplusAutomation

2021 ◽  
Author(s):  
Adam C Garber
Keyword(s):  
Auxiliary Variable ◽  
Integration Methods ◽  
Variable Integration ◽  
Biased Estimates ◽  
Multi Step Methods

This R tutorial automates the 3-step ML axiliary variable procedure using the MplusAutomation package (Hallquist & Wiley, 2018) to estimate models and extract relevant parameters. To learn more about auxiliary variable integration methods and why multi-step methods are necessary for producing un-biased estimates see Asparouhov & Muthén (2014). The motivation for writing this tutorial is that conducting the 3-step manually is highly error prone as it requires pulling logit values estimated in the step-1 model and adding them in the model statement of the step-2 model (i.e., lots of copying & pasting). In contrast, this approach is fully replicable and provides clear documentation which translates to more reliable research.

scholarly journals BCH Two-step Auxiliary Variable Integration with MplusAutomation

2021 ◽  
Author(s):  
Adam C Garber
Keyword(s):  
Auxiliary Variable ◽  
Mixture Modeling ◽  
Longitudinal Survey ◽  
Original Study ◽  
Data Repository ◽  
Auxiliary Variables ◽  
The Public ◽  
Variable Integration ◽  
Biased Estimates ◽  
Multi Step Methods

This R tutorial automates the BCH two-step axiliary variable procedure (Bolk, Croon, Hagenaars, 2004) using the MplusAutomation package (Hallquist & Wiley, 2018) to estimate models and extract relevant parameters. To learn more about auxiliary variable integration methods and why multi-step methods are necessary for producing un-biased estimates see Asparouhov & Muthén (2014). The name of this mehtod, BCH, stands for Bolck, Croon, & Hagenaars, the authors who developed this method (Bolk, Croon, Hagenaars, 2004). This tutorial utilizes the public-use data repository named the Longitudinal Survey of American Youth (LSAY; Miller et al., 1992). The applied example used in this tutorial is based off the example presented in the seminal chapter on mixture modeling by Katherine Masyn (2013). This tutorial contains the 9 math indicators from this original study as well as two auxiliary variables.

scholarly journals Improved second-order unconditionally stable schemes of linear multi-step and equivalent single-step integration methods

2020 ◽  
Author(s):  
Huimin Zhang ◽  
Runsen Zhang ◽  
Pierangelo Masarati
Keyword(s):  
Unconditional Stability ◽  
Single Step ◽  
Second Order ◽  
Step Method ◽  
Unconditionally Stable ◽  
Integration Methods ◽  
Optimal Accuracy ◽  
Intermediate Variables ◽  
First Time ◽  
Multi Step Methods

AbstractSecond-order unconditionally stable schemes of linear multi-step methods, and their equivalent single-step methods, are developed in this paper. The parameters of the linear two-, three-, and four-step methods are determined for optimal accuracy, unconditional stability and tunable algorithmic dissipation. The linear three- and four-step schemes are presented for the first time. As an alternative, corresponding single-step methods, spectrally equivalent to the multi-step ones, are developed by introducing the required intermediate variables. Their formulations are equivalent to that of the corresponding multi-step methods; their use is more convenient, owing to being self-starting. Compared with existing second-order methods, the proposed ones, especially the linear four-step method and its alternative single-step one, show higher accuracy for a given degree of algorithmic dissipation. The accuracy advantage and other properties of the newly developed schemes are demonstrated by several illustrative examples.

Examining Nonnormal Latent Variable Distributions for Non-Ignorable Missing Data

2021 ◽  
Vol 45 (3) ◽  
pp. 159-177
Author(s):  
Chen-Wei Liu
Keyword(s):  
Missing Data ◽  
Latent Variable ◽  
Bivariate Normal Distribution ◽  
Parameter Estimates ◽  
Missing Responses ◽  
Variable Distribution ◽  
Item Responses ◽  
Nonnormal Distribution ◽  
The Impact ◽  
Biased Estimates

Missing not at random (MNAR) modeling for non-ignorable missing responses usually assumes that the latent variable distribution is a bivariate normal distribution. Such an assumption is rarely verified and often employed as a standard in practice. Recent studies for “complete” item responses (i.e., no missing data) have shown that ignoring the nonnormal distribution of a unidimensional latent variable, especially skewed or bimodal, can yield biased estimates and misleading conclusion. However, dealing with the bivariate nonnormal latent variable distribution with present MNAR data has not been looked into. This article proposes to extend unidimensional empirical histogram and Davidian curve methods to simultaneously deal with nonnormal latent variable distribution and MNAR data. A simulation study is carried out to demonstrate the consequence of ignoring bivariate nonnormal distribution on parameter estimates, followed by an empirical analysis of “don’t know” item responses. The results presented in this article show that examining the assumption of bivariate nonnormal latent variable distribution should be considered as a routine for MNAR data to minimize the impact of nonnormality on parameter estimates.

scholarly journals A Traveler’s Guide to the Multiverse: Promises, Pitfalls, and a Framework for the Evaluation of Analytic Decisions

2021 ◽  
Vol 4 (1) ◽  
pp. 251524592095492
Author(s):  
Marco Del Giudice ◽  
Steven W. Gangestad
Keyword(s):  
Degrees Of Freedom ◽  
A Priori ◽  
Simulated Data ◽  
Style Analysis ◽  
Data Set ◽  
Scant Attention ◽  
Equivalence Type ◽  
The Impact ◽  
Biased Estimates

Decisions made by researchers while analyzing data (e.g., how to measure variables, how to handle outliers) are sometimes arbitrary, without an objective justification for choosing one alternative over another. Multiverse-style methods (e.g., specification curve, vibration of effects) estimate an effect across an entire set of possible specifications to expose the impact of hidden degrees of freedom and/or obtain robust, less biased estimates of the effect of interest. However, if specifications are not truly arbitrary, multiverse-style analyses can produce misleading results, potentially hiding meaningful effects within a mass of poorly justified alternatives. So far, a key question has received scant attention: How does one decide whether alternatives are arbitrary? We offer a framework and conceptual tools for doing so. We discuss three kinds of a priori nonequivalence among alternatives—measurement nonequivalence, effect nonequivalence, and power/precision nonequivalence. The criteria we review lead to three decision scenarios: Type E decisions (principled equivalence), Type N decisions (principled nonequivalence), and Type U decisions (uncertainty). In uncertain scenarios, multiverse-style analysis should be conducted in a deliberately exploratory fashion. The framework is discussed with reference to published examples and illustrated with the help of a simulated data set. Our framework will help researchers reap the benefits of multiverse-style methods while avoiding their pitfalls.

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