Applied Psychometric Strategies Lab Applied Quantitative and Psychometric

Applied Psychometric Strategies Lab Applied Quantitative and Psychometric Series David Dueber, MA Advanced Issues in Specifying Regression Models with Single Indicator Latent Variables April 19, 2018

Wrong syntax for SILV and observed variables in one model 2

Regression is a saturated model! 3

The right way to incorporate observed variables 4

Non-positive definite first-order derivative product matrix Cannot trust standard errors, and therefore cannot trust significance tests 5

Third time’s the charm: Bootstrapping to the rescue • Bootstrapping constructs an empirical sampling distribution and thereby estimates standard errors without referring to the expected information matrix • Confidence intervals can be computed using… – The boostrap SE and standard normal theory with “cinterval” – Percentile bootstrapping with “cinterval(bootstrap)” – Bootstrapping with bias correction with “cinterval(bcbootstrap)” 6

Finally, results! 7

Results! 8

Handling Missing data with auxiliary variables • Specify correlations between auxiliary variables and the other variables in the model – use the SILV for the predictors and outcome, not the observed variable name, which here represents the disturbance – Do not use the “auxiliary” command in the Variable: block 9

Output: Everything is Awesome! 10

What about interactions? • Bisbe, Coenders, Saris, & Batista-Foguet (2006) • Unreliable variance of XY is var(X)var(Y)*(1 -Rel(X)Rel(Y)) 11

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