We study a factor analysis model with two normally distributed observations and one factor. Two approximate conditional inference procedures for the factor loading are developed. The first proposal is a very simple procedure but it is not very accurate. The second proposal gives extremely accurate results even for very small sample size. Moreover, the calculations require only the signed log likelihood ratio statistic and a measure of the standardized maximum likelihood departure. Simulations are used to study the accuracy of the proposed procedures. Key words: canonical parameter, factor analysis model, signed log likelihood ratio statistic, standardized maximum likelihood departure 1 1. Introduction Let (x; y) 0 be a two-dimensional vector of observable variables and let f be one-dimensional. The factor analysis model studied by Laake (1988) and Anderson & Laake (1998), can be written as 0 B @ x y 1 C A = 0 B @ x y 1 C A + 0 B @ 1 fi 1 C A f + 0 B @ u v 1 C A (1) ..
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