Fig. 5

Mathematical model for the item responses for Generalized Anxiety Disorder-7. A The blue line illustrates the pattern of the model of the item responses for such scales. When the relative frequency of “several days,” the ratio of “more than half the days” to “several days,” and the ratio of “nearly every day” to “more than half the days” are presented as P₁, r_1, and r₂, respectively, the relative frequencies of “not at all,” “several days,” “more than half the days,” and “nearly every day” are expressed as 1 − P₁ × (1 + r₁ + r₁r₂), P₁, P₁r₁, and P₁r₁r₂, respectively. B The relative frequencies of “not at all,” “several days,” “more than half the days,” and “nearly every day” for another item (the red line) are expressed as 1 – P₂ × (1 + r₁ + r₁r₂), P₂, P₂r₁, and P₂r₁r₂, respectively. According to the calculation, the intersection between “not at all” and “several days,” is expressed as follows: (x, y) = (\(\frac{\text{r}1\text{r}2 + \text{r}1 + 1}{\text{r}1\text{r}2 + \text{r}1 + 2}\), \(\frac{1}{\text{r}1\text{r}2 + \text{r}1 + 2}\)). C A line chart model of the item responses between “several days” and “nearly every day” on a logarithmic scale. On the logarithmic scale, the relative frequencies of “several days,” “more than half the days,” and “nearly every day” for the blue line are expressed as logP₁, logP₁ + logr₁, and logP₁ + logr₁ + logr_2, respectively. Consequently, the slopes from “several days” to “more than half the days,” and from “more than half the days” to “nearly every day” are expressed as logr₁ and logr₂, respectively