tppcm - Step Discriminations for the Two-Parameter Partial Credit Model on Top of 'TAM'

In the two-parameter partial credit model (TPPCM) of Yu (1991) <https://hdl.handle.net/2142/21459>, every step of a polytomous item has its own discrimination. Estimation is left to existing software: 'TAM' (tam.mml.3pl() with a step design matrix, tam.mml.2pl(), tam.mml()) and, for the bilinear product form and non-negativity constraints, 'sirt' (xxirt()). The package adds what these packages do not provide: standard errors of step discriminations based on the full observed information, step-level Wald tests, and score tests with modification indices and expected parameter changes for moving down the model ladder saturated TPPCM -> product form -> generalized partial credit model -> partial credit model, limited-information fit statistics (the M2 statistic, root mean square error of approximation, standardized root mean squared residual, comparative fit index and Tucker-Lewis index; Maydeu-Olivares and Joe (2006) <doi:10.1007/s11336-005-1295-9>) for any step design, step contributions to the item information, and tests of differential step functioning across groups: per-step Lagrange multiplier tests from one multigroup fit (Glas (1998) <https://www3.stat.sinica.edu.tw/statistica/j8n3/j8n32/j8n32.htm>), with the generalized score test of Boos (1992) <doi:10.1080/00031305.1992.10475921>, likelihood ratio tests with configural, metric, scalar and partial multigroup designs, score-based tests (Merkle and Zeileis (2013) <doi:10.1007/s11336-012-9302-4>) and model-based trees (Zeileis, Hothorn and Hornik (2008) <doi:10.1198/106186008X319331>). The generalized partial credit model of Muraki (1992) <doi:10.1177/014662169201600206> is the special case with equal steps within items.