Quantification methods which consist of types 1, 2, 3, 4 are basic for statistical analysis of qualitative data such as questionnaires data, etc. Upon quantifying qualitative data by introducing dummy variables of 0 and 1, Type 1 and 2 may be regarded as regression analysis and discriminant analysis respectively. In this paper we propose a test statistic for additional information in Type 2, based on sample scores. It is shown that the test statistic is essentially the same as the ones for additional information in regression analysis and discriminant analysis. Therefore, it may be noted that the validity of F-approximation for the test statistic in Type 2 can be examined by checking a normal approximation of residuals in regression analysis and by this, we will numerically validate the fit of test statistic's F approximation. Also, in Type 2, we will reflect sequential variable selection method using additional information test and variable selection methods based on model selection criteria, which have been established in regression analysis, and try to numerically validate these.

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Varying coefficients can be used for visualizations or interpretations of the covariate effects which might be varying on time axis. The estimator of varying coefficient is usually obtained by kernel smoothing methods. Since it is essentially the linear regression around fixed time point, constructing a confidence interval or testing null hypothesis for a function of time is difficult. In this paper, we apply an estimating method proposed by Satoh and Yanagihara (2008) on the growth curve model to the discrete distributions using generalized estimating equations. Those new estimators of varying coefficients can be easily calculated by the ordinaly statistical software package. An example of logistic regression analysis with longitudinal data was illustrated.

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