Pseudo-Likelihood Estimation of Log-Multiplicative Association Models
Computes statistics to assess convergence of the nominal model
Computes statistics to assess convergence for generalized partial cred...
Checks for basic errors in input to the 'ple.lma' function
Fits LMA model where category scale values equal a_im * x_j
Fits the log-linear model of independence
Fits the nominal model
Fits an LMA using fixed category scores
Up-dates association parameters of the nominal model
Up-dates association parameters of the GPCM by fitting model to stacke...
Estimates item parameters of LMA with linear restrictions on category ...
Prepares data for up-dating scale value parameters of nominal model
Creates data frame up-dating phi parameters of the gpcm.
loops through items and up-dates estimates of scale values for each it...
Plots estimated parameters by iteration for the gpcm and nominal model...
Produces a summary of results
Main function for estimating parameters of LMA models
Re-scales the category scale values and Phi after convergence of the n...
Imposes scaling constraint to identify parameters of the LMA (nominal)...
Imposes scaling constraint to identify parameters of LMA (GPCM)
Graphs estimated scale values by integers of the LMA (nominal) model
Sets up the data based on input data and model specifications
Prepares data for up-dating association parameters of a multidimension...
Prepares data for up-dating association parameters of LMA (GPCM) model
Computes estimates of theta (values on latent trait(s)) for all LMA mo...
Log-multiplicative association models (LMA) are models for cross-classifications of categorical variables where interactions are represented by products of category scale values and an association parameter. Maximum likelihood estimation (MLE) fails for moderate to large numbers of categorical variables. The 'pleLMA' package overcomes this limitation of MLE by using pseudo-likelihood estimation to fit the models to small or large cross-classifications dichotomous or multi-category variables. Originally proposed by Besag (1974, <doi:10.1111/j.2517-6161.1974.tb00999.x>), pseudo-likelihood estimation takes large complex models and breaks it down into smaller ones. Rather than maximizing the likelihood of the joint distribution of all the variables, a pseudo-likelihood function, which is the product likelihoods from conditional distributions, is maximized. LMA models can be derived from a number of different frameworks including (but not limited to) graphical models and uni-dimensional and multi-dimensional item response theory models. More details about the models and estimation can be found in the vignette.