THE STATISTICAL-ANALYSIS OF GENERAL PROCESSING TREE MODELS WITH THE EM ALGORITHM

被引:263
作者
HU, X
BATCHELDER, WH
机构
[1] School of Social Sciences, University of California, Irvine, 92717, CA
关键词
EM ALGORITHM; MULTINOMIAL MODELS; PROCESSING TREES; POWER DIVERGENCE FAMILY;
D O I
10.1007/BF02294263
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Multinomial processing tree models assume that an observed behavior category can arise from one or more processing sequences represented as branches in a tree. These models form a subclass of parametric, multinomial models, and they provide a substantively motivated alternative to loglinear models. We consider the usual case where branch probabilities are products of nonnegative integer powers in the parameters, 0 less-than-or-equal-to theta(s) less-than-or-equal-to 1, and their complements, 1 - theta(s). A version of the EM algorithm is constructed that has very strong properties. First, the E-step and the M-step are both analytic and computationally easy; therefore, a fast PC program can be constructed for obtaining MLEs for large numbers of parameters. Second, a closed form expression for the observed Fisher information matrix is obtained for the entire class. Third, it is proved that the algorithm necessarily converges to a local maximum, and this is a stronger result than for the exponential family as a whole. Fourth, we show how the algorithm can handle quite general hypothesis tests concerning restrictions on the model parameters. Fifth, we extend the algorithm to handle the Read and Cressie power divergence family of goodness-of-fit statistics. The paper includes an example to illustrate some of these results.
引用
收藏
页码:21 / 47
页数:27
相关论文
共 26 条
[1]  
[Anonymous], 1901, WIEN KLIN WOCHENSCHR
[2]   MULTINOMIAL PROCESSING MODELS OF SOURCE MONITORING [J].
BATCHELDER, WH ;
RIEFER, DM .
PSYCHOLOGICAL REVIEW, 1990, 97 (04) :548-564
[3]   THE STATISTICAL-ANALYSIS OF A MODEL FOR STORAGE AND RETRIEVAL-PROCESSES IN HUMAN-MEMORY [J].
BATCHELDER, WH ;
RIEFER, DM .
BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY, 1986, 39 :129-149
[4]   GOODNESS-OF-FIT STATISTICS FOR DISCRETE MULTIVARIATE DATA - READ,TRC, CRESSIE,NAC [J].
BATCHELDER, WH .
JOURNAL OF MATHEMATICAL PSYCHOLOGY, 1991, 35 (02) :267-273
[5]   EXPERIMENTAL-ANALYSIS OF STORAGE AND RETRIEVAL-PROCESSES INVOLVED IN RETROACTIVE-INHIBITION - THE EFFECT OF PRESENTATION MODE [J].
BAUML, KH .
ACTA PSYCHOLOGICA, 1991, 77 (02) :103-119
[6]  
Bernstein F., 1925, Z ABSTAMMUNGS UND VE, V37, P237, DOI [10.1007/BF01763333, DOI 10.1007/BF01763333]
[7]  
BOYLES RA, 1983, J ROY STAT SOC B MET, V45, P47
[8]  
CEPPELLINI R, 1955, ANN HUM GENET, V20, P97
[9]   BAYESIAN PROCEDURE FOR SEPARATELY ESTIMATING STORAGE AND RETRIEVAL COMPONENTS OF FORGETTING [J].
CHECHILE, R ;
MEYER, DL .
JOURNAL OF MATHEMATICAL PSYCHOLOGY, 1976, 13 (03) :269-295
[10]   MAXIMUM LIKELIHOOD FROM INCOMPLETE DATA VIA EM ALGORITHM [J].
DEMPSTER, AP ;
LAIRD, NM ;
RUBIN, DB .
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-METHODOLOGICAL, 1977, 39 (01) :1-38