PSYCHOMETRIKA--VOL. 50, NO. 2, 229-242 JUNE 1985 NONCONVERGENCE, IMPROPER SOLUTIONS, AND STARTING VALUES IN LISREL MAXIMUM LIKELIHOOD ESTIMATION ANNE BOOMSMA UNIVERSITYOF GRONINGEN In the framework of a robustness study on maximum likelihood estimation with LISREL three types of problems are dealt with: nonconvergence,improper solutions, and choice of start- ing values. The purpose of the paper is to illustrate why and to what extent these problems are of importance for users of LISREL. The ways in which these issues may affect the design and con- clusions of robustness research is also discussed. Key words: maximum likelihood estimation, LISREL, Davidon-Fletcher-Powell, starting values, nonconvergence,improper solutions, robustness, Monte Carlo, small sample results. Introduction In studies on the robustness of maximum likelihood estimation with LISREL, the effects of small sample size and those of nonnormal, discrete distributions were investi- gated (Boomsma, 1982, 1983). Three main conclusions from that research were made. (i) In LISREL modeling it is recommended not to use a sample size smaller than 100. (ii) LISREL is robust against symmetric, discrete distributions with normal kurtosis, but not against rather skewed, discrete distributions. (iii) It is not recommended to analyze corre- lation matrices instead of covariance matrices, because it may have serious effects on the estimated covariances of the parameter estimates. The present paper deals with three problems encountered during the work just re- ferred to: nonconvergence of the iterative maximum likelihood estimation, improper pa- rameter estimates, and the choice of starting values in the estimation process. The results discussed below indicate that users of LISREL should be aware of cir- cumstances in which nonconvergence and improper solutions may occur, and their fre- quency of occurrence. They may also be interested in the effect of the starting values in iterative estimation. Some of the materials presented may serve as guidelines for re- searchers planning Monte Carlo studies. The emphasis in this paper will be on the practi- cal implications of the findings for users of LISREL, illustrated by results from Monte Carlo work. Monte Carlo design. The sampling design for the small sample part of our study is summarized as follows. In the LISREL framework for each specified model with a known population parameter vector to, a population covariance matrix ~ is defined. These matrices ~ are the covariance structures of multivariate normal distributions from which independent samples were taken of size 25, 50, 100, 200, and 400. For each model and each sample size N, NRS > 300 samples were taken (NRS = number of replications in stock). The samples were generated by using subroutine GGNMS from IMSL (1982) on a CDC Cyber 74/18 and a CDC Cyber 170/760 machine. Thus, for each model and each sample size, NRS sample covariance matrices S were obtained. After this sampling process a LISREL analysis was done for each S until NR = 300 samples have led to a solution without numerical difficulties; for all N this number of Requests for reprints should be sent to A. Boomsma, Vakgroep Statistiek en Meettheorie, Rijksuniversiteit Groningen, Oude Boteringestraat 23, 9712 GC Groningen, THE NETHERLANDS. 0033- 3123/85/0600- 5010500. 75/0 229 © 1985The Psychometric Society