Sample size

Facets produces estimates for any data set in which there is overlapping randomness in the observations across elements. It cannot estimate measures when the data have a Guttman pattern or there is only one observation element. But even in these cases, anchoring and other analytical technique may make the element measures estimable.

 

Estimates which are likely to have some degree of stability across samples require at least 30 observations per element, and at least 10 observations per rating-scale category.

 

There is no maximum sample size apart from those imposed by computer constraints. Large sample sizes tend to make convergence slower and fit statistics overly sensitive.

 

Estimation technique

Facets uses JMLE (= Joint Maximum-Likelihood Estimation), implemented with iterative-curve fitting, rather than Newton-Raphson estimation, because iterative curve-fitting is more robust against awkward data patterns.
 
Every estimation method has strengths and weaknesses. The primary weakness of JMLE is that estimates have statistical bias. This is most obvious in a test of two dichotomous items (Andersen, 1973). In such a test, the difference between the item difficulties of the two items will be estimated to be twice its true value. In practical situations, the statistical bias is usually less than the standard errors of the estimates . However, the advantages of JMLE far outweigh its disadvantages. JMLE is estimable under almost all conditions including arbitrary and accidental patterns of missing data, arbitrary anchoring (fixing) of parameter estimates, unobserved intermediate categories in rating scales, and multiple different Rasch models in the same analysis.

 

RSA and MFRM derive Newton-Raphson iteration equations for the estimation of Rasch measures using the JMLE approach. In Facets, this approach is not robust enough against spikey data. Consequently, since the basic functional shape of all the estimation equations is the logistic ogive, Facets estimates measures by means of iterative curve-fitting to that shape. The resulting measures also accord with the JMLE approach.

 

Andersen, E. B. Conditional inference for multiple-choice questionnaires. British Journal of Mathematical and Statistical Psychology, 1973, 26, 31-44.