Item response diagnostics: unpredictable voters, Lord's DIF test, SE of theta and average variance extracted
Source:R/IrtDiagnostics.R
Hsirt.RdR arm of morie.fn.hsirt, lordzs, semthe and
ave. Hsirt: Lauderdale's heteroskedastic probit, per
legislator scales \(\psi_i\) in \(\Phi((\beta_j x_i - \alpha_j)/\psi_i)\)
given ideal points, alternating probit Fisher scoring for the items and
Brent plus Newton for each \(\log\psi_i\), geometric mean of psi 1;
posterior mode under normal priors of standard deviation
psi_prior_sd on log psi and item_prior_sd on the items (NULL
for plain ML, which is degenerate for perfectly predicted voters).
Lordzs: Lord's chi-square test of equal item parameters in two
groups, \(d'(\Sigma_R + \Sigma_F)^{-1} d\). Semthe: standard
error of an ability estimate from the 2PL test information.
Ave: average variance extracted, the mean squared standardised
loading.
Usage
Hsirt(
votes,
ideal_points,
item_params = NULL,
max_iter = 50,
psi_prior_sd = 1,
item_prior_sd = 5
)
Lordzs(b_R, b_F, V_R, V_F = NULL)
Semthe(theta, items)
Ave(loads)Arguments
- votes
Binary vote matrix (NA missing).
- ideal_points
Fixed ideal points.
- item_params
Optional list of alpha and beta vectors.
- max_iter
Alternation rounds.
- psi_prior_sd
Prior standard deviation of log psi.
- item_prior_sd
Prior standard deviation of the item parameters.
- b_R, b_F
Item parameters in the reference and focal groups.
- V_R, V_F
Their covariances (V_R alone is the summed covariance).
- theta
Ability value(s).
- items
Two-column matrix of (a, b) item parameters.
- loads
Standardised factor loadings.
References
Lauderdale, B. E. (2010). Unpredictable voters in ideal point estimation. Political Analysis 18, 151-171.
Lord, F. M. (1980). Applications of Item Response Theory to Practical Testing Problems. Erlbaum.
Fornell, C. and Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research 18, 39-50.