DISCUSSION ON A MODEL OF TWO TURNING POINTS AS EXPRESSION OF INDIVIDUAL VARIATION

Using lighting experiment of adjustment method

Abstract

 Many human-environmental models were proposed by researchers of environmental psychology and surrounding fields, in order to deepen the understanding. Proposal of those models often defines and differentiate similar conditions and/or expand the usage of the former proposed model. For example, Kuno et al proposed two-dimensional thermal sensation model that introduced surrounding environmental index axis and thermal physiological index model, which differentiated “hot” to “warm” and “comfort” to “pleasant”. Likely, model of two turning points introduced by Hirate et al differentiated the type of decision, namely one turning point and two turning points. One turning point is where decision only changes once, like good / bad. Two turning points was where decision changes twice, like bad / good / bad, which indicates the adequate range. In addition, this model was developed from model proposed by Thustone, which adapted the model to experiments done by pairwise comparison method. Hirate et al not only introduced the model with two turning points as an expansion of the model, but also developed the model to explaining the experimental results of semantic differential method.

 In chapter 2, model of two turning points is explained to discuss the limits and problem it holds. Two problems were shown. One is the premises of homoscedasticity, and second is the application to the experiment conducted using semantic differential method. To verify homoscedasticity (chapter 3), Bartlett test was conducted using data of pleasant lighting environment experiment obtained by adjustment method. As a result, homoscedasticity wasn’t shown under several bright conditions. In case of experimenting under broad range, this premise might not be fulfilled. However, there are two mathematical importance to this model. One is that P distribution is obtained by two times integration of R distribution (Eq. 5). Other is that this model can be interpreted by cumulative distribution function with the average of the true reaction (Eq. 6). To test the latter importance, goodness of fit test was conducted with normal distribution and logistic distribution. Both distributions fitted, and to expand the application of the model, the data was applied using multinomial logistic analysis and sequential logistic analysis. Both applied, which showed the possibility of adapting the model to non-equal variance data.

 In chapter 4, the first mathematical importance was verified, using quartic function. If P distribution was obtained by two times integration of the R distribution, then known P distribution may be used to calculate the unknown R distribution. By setting the inflection points as two turning points, quartic function is applied to the known P distribution, and two times differentiation was done to obtain unknown two turning points. Further considerations on constraint condition has to be done, yet expansion of the model was shown.

 The model with two turning points was re-considered using the data obtained by adjustment method. Unlike the premises of the model, homoscedasticity was not proven, yet through adaptation of logistic analysis, it was shown that model can be applied to cases of non-equal variance. In addition, through mathematical analysis, quartic function was applied and two unknown turning points were calculated, showing the new application of the model.