Posts

Alignment Optimization with `mirt`

A note on alignment optimization with mirt output, and obtaining factor scores

Bayesian Multilevel Factor Model (Part I)

Comparing different approaches for fitting multilevel factor models with random intercepts

Multilevel SEM using estimated level-specifc covariance matrices

Demonstration of conducting MSEM using level-specific covariance matrices without raw data

Variance explained for contrasts

Learning note of using contrast matrix for sum of squares

Monte Carlo Simulation with Julia (Growth Model)

Learning note of using Julia for simulation

Power Analysis: An Example with a Latent Change Score Model

A power analysis and power curve example on the difference in change rate across treatment conditions with a latent change score model.

Multilevel Composite Reliability

This is a short blog post on computing multilevel reliability based on Lai (2021).

Nominal Regression in STAN

I was talking to a colleague about modeling nominal outcomes in STAN, and wrote up this example. Just put it here in case it’s helpful for anyone (probably myself in the…

Scaling and Standard Errors in SEM

In this post, I demonstrate why rescaling a coefficient (i.e., multiplied/divided by a constant) is different from “standardizing” a coefficient (i.e., multiplied/divided by…

Estimating a 2-PL Model in Julia (Part 2)

\[ \newcommand{\bv}[1]{\boldsymbol{\mathbf{#1}}} \]

Estimating a 2-PL Model in Julia (Part 1)

The semester is finally over, and for some reason, I wanted to consolidate my understanding of some psychometric models, perhaps because I’ll be teaching a graduate…

Confidence Intervals for Multilevel R-Squared

The marginal \(R^2\) considers the total variance accounted for due to the fixed effect associated with the predictors (Days in this example). See Nakagawa, Johnson, &…

Actor Partner Interdependence Model With Multilevel Analysis

Every time I teach multilevel modeling (MLM) at USC, I have students interested in running the actor partner independence model (APIM) using dyadic model. While such models…

IRT Scoring With Covariates

I was working on an extension to the two-stage path analysis Lai & Hsiao (2021) related to integrative data analysis, and ran into an issue described in Davoudzadeh et…

Using cmdstanr in SimDesign

[Update: Use parallel computing with two cores.]

Mixed Factorial ANOVA in R

The fictional data set is part of the data library of the JASP software, and is from the book by Field (2017)¹. Here it only contains a subset of the data, where 10 men and…

Unit-Specific vs. Population-Average Models

One thing that I always felt uncomfortable in multilevel modeling (MLM) is the concept of a unit-specific (US)/subject-specific model vs. a population-average (PA) model.…

Piping with `magrittr`

I have just spent a semester teaching multilevel modeling, and in the R codes I provided, I usually use the pipe operator (%>%). For example, to compute the cluster means…

Potential Fit and Application Tips

This post was first written in 2020, with an update on rubric in 2022.

Weighted Least Squares

Recently I was working on a revision for a paper that involves structural equation modeling with categorical observed variables, and it uses a robust variant of weighted…

Asymptotic Standard Errors in CFA

In our lab meeting I’m going to present the article by Maydeu-Olivares (2017), which talked about standard errors (SEs) of the maximum likelihood estimators (MLEs) in SEM…

Using Julia to Find MLE for a Factor Model

I’ve been staying home for a bit more than a week now. While keep working on my research, I also think it may help fill my time by picking up some skills. I’ve been…

Model Selection for Multilevel Modeling

In social sciences, many times we use statistical methods to answer well-defined research questions that are derived from some theory or previous research. For example…

Bayesian MLM With Group Mean Centering

This post is re-rendered on 2024-03-21 with cleaner and more efficient STAN code.