Showing papers on "Probabilistic latent semantic analysis published in 1985"

Constrained latent class models: Theory and applications

Abstract: Three types of restricted latent class models for binary data are discussed: models assuming equalities of certain latent parameters, linearly constrained latent class analysis, and linear logistic latent class analysis. The basic equations of the latter model state the decomposition of the log odds of the item latent probabilities and of the class sizes into weighted sums of basic parameters representing the effects of predictor variables which are hypothesized to be relevant indicators for the original parameters. The maximum likelihood equations for these effect parameters and a criterion for their local identifiability are given. Further, statistical tests for goodness of fit are sketched, and the practical application of linear logistic latent class analysis is demonstrated by several examples. They comprise some known scaling models as well as a simple model with located classes and items, a model which relates item difficulty to item structure, and a model for measuring latent changes. Finally, the generalization of linear logistic latent class analysis to polytomous manifest variables is outlined.

A comparison of latent trait and latent class analyses of Likert-type data

Abstract: This paper brings together and compares two developments in the analysis of Likert attitude scales. The first is the generalization of latent class models to ordered response categories. The second is the introduction of latent trait models with multiplicative parameter structures for the analysis of rating scales. Key similarities and differences between these two methods are described and illustrated by applying a latent trait model and a latent class model to the analysis of a set of “life satisfaction” data. The way in which the latent trait model defines a unit of measurement, takes into account the order of the response categories, and scales the latent classes, is discussed. While the latent class model provides better fit to these data, this is achieved at the cost of a logically inconsistent assignment of individuals to latent classes.

Nondeterministic versus probabilistic linear search algorithms

Abstract: The "component counting lower bound" known for deterministic linear search algorithms (LSA's) also holds for their probabilistic versions (PLSA's) for many problems, even if two-sided error is allowed, and if one does not charge for probabilistic choice. This implies lower bounds on PLSA's for e.g. the element distinctness problem (n log n) or the knapsack problem (n2). These results yield the first separations between probabilistic and non-deterministic LSA's, because the above problems are non-deterministically much easier. Previous lower bounds for PLSA's either only worked for one-sided error "on the nice side", i.e. on the side where the problems are even non-deterministically hard, or only for probabilistic comparison trees. The proof of the lower bound differs fundamentally from all known lower bounds for LSA's or PLSA's, because it does not reduce the problem to a combinatorial one but argues extensively about e.g. a non-discrete measure for similarity of sets in Rn. This lower bound result solves an open problem posed by Manber and Tompa as well as by Snir. Furthermore, a PLSA for n input variables with two-sided error and expected runtime T can be simulated by a (deterministic) LSA in T2n steps. This proves that the gaps between probabilistic and deterministic LSA's shown by Snir cannot be too large. As this simulation even holds for algebraic computation trees we show that probabilistic and deterministic versions of this model are polynomially related. This is a weaker version of a result due to the author which shows that in case of LSA's, even the non-deterministic and deterministic versions are polynomially related.

A time-dependent latent class analysis based on states-transition

Abstract: Two types of new latent class model are proposed for questionnaires observed at several time-points, where existence of certain tilne-dependent latent classes is assumed. The authors concretely derive the EM algorithm to obtain maximum likelihood estimates of latent parameters in the respective models, such as mixed proportions and identified states-transitioll parameters of the respective Iatent classes. The merit of the algorithm derived here is that the resultant estimates can not be improter solutions. Also, the goodness of fit test is given with some numerical examples. The FORTRAN software is available from the authors.