  When the item functioning of multi-item measurement is modeled with three or
four-parameter models, parameter estimation may become challenging. Effective
algorithms are crucial in such scenarios. This paper explores innovations to
parameter estimation in generalized logistic regression models, which may be
used in item response modeling to account for guessing/pretending or
slipping/dissimulation and for the effect of covariates. We introduce a new
implementation of the EM algorithm and propose a new algorithm based on the
parametrized link function. The two novel iterative algorithms are compared to
existing methods in a simulation study. Additionally, the study examines
software implementation, including the specification of initial values for
numerical algorithms and asymptotic properties with an estimation of standard
errors. Overall, the newly proposed algorithm based on the parametrized link
function outperforms other procedures, especially for small sample sizes.
Moreover, the newly implemented EM algorithm provides additional information
regarding respondents' inclination to guess or pretend and slip or dissimulate
when answering the item. The study also discusses applications of the methods
in the context of the detection of differential item functioning. Methods are
demonstrated using real data from psychological and educational assessments.
