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Last data update: 2014.03.03

R: Data generation

gendat

R Documentation

Data generation

Description

Computation of association probabilities and data generation for disjunctive or conjunctive probabilistic latent feature models.

Usage

gendat(maprule="disj", N, objpar, attpar)

Arguments

`maprule`	Disjunctive (`maprule="disj"`) or conjunctive (`maprule="conj"`) mapping rule of the probabilistic latent feature model.
`N`	Number of replications for which binary associations are generated.
`objpar`	True objectparameters. As object parameters are probabilities they should be between 0 and 1.
`attpar`	True attributeparameters. As attribute parameters are probabilities they should be between 0 and 1.

Details

The function gendat computes for all pairs of J objects and K attributes association probabilities and it generates association frequencies (i.e. the number of replications N for which an object is associated to an attribute), according to a disjunctive or a conjunctive probabilistic latent feature model. In addition, the function computes a matrix with in each cell the total number of replications N. If the requested number of replications N equals 0, the function only computes association probabilities and does not generate new data.

To compute association probabilities the function gendat uses a J X F matrix of object parameters and a K X F matrix of attribute parameters as input. The F object parameters of object j represent, for each of F features, the probability that object j has feature f. Similarly, the F attribute parameters of attribute k reflect, for each of F features, the probability that attribute k is linked to feature f.

According to the disjunctive probabilistic latent feature model, object j is associated to attribute k if the object and the attribute have at least one feature in common. More specifically, the association probability in cell (j,k) for the disjunctive model can be computed as:

p(j,k)=1-∏_f(1-objpar[j,f]*attpar[k,f]).

According to the conjunctive probabilistic latent feature model, object j and attribute k are associated if object j has all the features that are linked to attribute k. For the conjunctive model the association probability in cell (j,k) is computed as:

p(j,k)=∏_f(1-(1-objpar[j,f])*attpar[k,f]).

Value

`call`	Parameters used to call the function.
`prob1`	J X K matrix of association probabilities.
`freq1`	J X K matrix of association frequencies.
`freqtot`	J X K matrix with number of replications.

Author(s)

Michel Meulders

References

Maris, E., De Boeck, P., and Van Mechelen, I. (1996). Probability matrix decomposition models. Psychometrika, 61, 7-29.

Meulders, M., De Boeck, P., Van Mechelen, I., Gelman, A., and Maris, E. (2001). Bayesian inference with probability matrix decomposition models. Journal of Educational and Behavioral Statistics, 26, 153-179.

Meulders, M., De Boeck, P., Van Mechelen, I., & Gelman, A. (2005). Probabilistic feature analysis of facial perception of emotions. Applied Statistics, 54, 781-793.

Examples

## define constants
J<-20
K<-15
F<-2

## generate true parameters
set.seed(43565)
objectparameters<-matrix(runif(J*F),nrow=J)
attributeparameters<-matrix(runif(K*F),nrow=K)

## compute association probabilities for a conjunctive model
probconj<-gendat(maprule="conj",N=0,
             objpar=objectparameters,attpar=attributeparameters)

## generate data for a disjunctive model using N=200 replications
gdat<-gendat(maprule="disj",N=200,
             objpar=objectparameters,attpar=attributeparameters)