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 future).

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 the sample standard deviation, which is a random variable) in SEM.

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

E-Step M-Step Estimating a 2-PL Model with EM in Julia Find \(\bar r_{jk}\) and \(\bar n_k\) Solve estimating equations Iterations Stopping criteria Benchmarking Remark \[ \newcommand{\bv}[1]{\boldsymbol{\mathbf{#1}}} \]

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

Import Data Two-Parameter Logistic Model Estimation with mirt in R Marginal Maximum Likelihood (MML) Estimation Implement MML Estimation in Julia Import R data Compute marginal loglikelihood Optimization Benchmarking 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 measurement class soon.

Confidence Intervals for Multilevel R-Squared

Load Packages An Example Multilevel Model Nakagawa-Johnson-Schielzeth \(R^2\) Right-Sterba \(R^2\) Confidence Intervals for \(R^2\) Parametric Bootstrap Bias-corrected estimate Confidence intervals Residual Bootstrap Confidence Intervals Bootstrap CI With Transformation Conclusion Load Packages library(lme4) ## Loading required package: Matrix library(MuMIn) # for computing multilevel R-squared library(r2mlm) # another package for R-squared ## Loading required package: nlme ## ## Attaching package: 'nlme' ## The following object is masked from 'package:lme4': ## ## lmList ## Registered S3 method overwritten by 'parameters': ## method from ## format.

Correcting for unreliability and partial invariance: A two-stage path analysis approach

Actor Partner Interdependence Model With Multilevel Analysis

Load Packages Data Hypothetical Research Question Distinguishable Dyads Indistinguishable Dyads Model Comparison Using SEM Distinguishable Dyads Indistinguishable Dyads Every time I teach multilevel modeling (MLM) at USC, I have students interested in running the actor partner independence model (APIM) using dyadic model.

What to Do If Measurement Invariance Does Not Hold? Let's Look at the Practical Significance

Measurement invariance---that a test measures the same construct in the same way across subgroups---needs to hold for subgroup comparisons to be meaningful. There has been tremendous growth in measurement invariance research in the past decade. …

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 al.

Using cmdstanr in SimDesign

library(SimDesign) library(cmdstanr) [Update: Use parallel computing with two cores.] Adapted from See for using cmdstanr Design <- createDesign(sample_size = c(30, 60, 120, 240), distribution = c('norm', 'chi')) Design ## # A tibble: 8 × 2 ## sample_size distribution ## <dbl> <chr> ## 1 30 norm ## 2 60 norm ## 3 120 norm ## 4 240 norm ## 5 30 chi ## 6 60 chi ## 7 120 chi ## 8 240 chi Generate <- function(condition, fixed_objects = NULL) { N <- condition$sample_size dist <- condition$distribution if(dist == 'norm'){ dat <- rnorm(N, mean = 3) } else if(dist == 'chi'){ dat <- rchisq(N, df = 3) } dat } Define Bayes estimator of the mean with STAN