The psychometric properties associated with the "specific objectivity" of the simple logistic model are acknowledged to be far superior to those of competing models. It is therefore the ideal model to be used for test development or for the analysis of any measuring instrument developed within a well-defined psychological construct. In estimating the model's parameters, relevant questions addressed are whether the data conform to the model well enough to be useful and how to protect estimates from disturbances to the measurement process specific to individual subjects and items. Fit analysis is considered within the central model concept of Rasch's specific objectivity; parameter estimates are invariant over particular situations. Alternative fit statistics methods are discussed, particularly the chi-square using biased and unbiased condition estimates. The CALFIT program and development of the BICAL program using chi square fit statistics are described. The total unweighted fit statistic in between-score group statistics considers the fundamental data matrix of fit analysis. Between-groups analysis should account for possible subsets that are potentially dangerous to measurement. No one statistic is necessary for every analysis and none by itself is sufficient to ensure specific objectivity which depends on analyses sensitive to possible disturbances. (CM)