CHAPTER 1 Introduction
4.4 Statistical tools
The main objective of the study is to determine the underlying dimensions which affect QOL. It is obvious that the demarcation of the domains of life are somewhat determined by all the above mentioned variables. It is also possible that there are correlations among all variables. However, given the set of original questions, factor analysis allows not only for a reduction of dimensions, but also for a good demarcation of the domains on the basis of clustering together those questions with similar information and setting apart those questions with different information. For this reason, factor analysis can be used to identify group of questions which provide correlated attributes of environment and which can be labeled as non arbitrary demarcation of dimension of life. Factor analysis can explore the covariance relationships among many variables in terms of a few underlying but unobservable random quantities called factors (Hair et al., 2005). The justification behind use of factor analysiscomes from the fact that large number of variables increases the possibility that the variables are not all uncorrelated and representative of distinct concepts. Instead, group of variables may be interrelated to the extent that they are all representative of more general concept. That is, variables within a particular group may be highly correlated among themselves but have relatively small correlation with variables in a different group. It is conceivable that each group of variables represented a single underlying construct, or factor, that is responsible for the observed correlation.
After identifying the dimensions it is practical to construct a single variable to represent the various dimensions of QOL. Principal components technique has been used to create the new variables and a regression method has been used to calculate the factor scores (Rojas, 2006 and Rojas, 2008). The main concept of principal component is summarization of information. Principal component is concerned with explaining
variables. In principal component, a set of variables have been transformed into some linear combinations of the original variables so that the resulting composite variables as a set might have maximum variance under the restriction that different linear composites are orthogonal to each other.
Secondly to find the significant factors which affect QOL, ordered probit regression analysis has been applied. This type of regression has been used because the dependent variable is an ordinal variable. In ordered probit analysis, the probability of an outcome is calculated as a linear function of the independent variables plus a set of cut points.
Let us assume that our ordered responses are denoted by Y*. The objective is to model these ordered responses as functions of explanatory variables. Here, the latent scale corresponds to the observed responses Yi which has five categories. The ordered response model in this case is motivated by an underlying continuous but latent process Y*
together with the response mechanism of the given form- Yi = 1 if Yi* < γ1
Yi = 2 if γ1 < Yi* < γ2 Yi = 3 if γ2 < Yi*
< γ3
Yi = 4 if γ3 < Yi* < γ4 Yi = 5 if γ4 < Yi*
The model is
i i
i X
Y* =β/ +µ ………..(1)
Now β and γ parameters have to be estimated. The γs are cut points that indicate the discrete category that the latent variable falls into. The latent variable Y* is related linearly to observable and unobservable factor and the latter have a fully specified distribution for f (µ) with zero mean and constant variance. Equation (1) gives the significant factors of QOL (Boes et al., 2006).
After obtaining the significant factors, it would be required to see if factors are explained by differential effect of area or income groups. Therefore, a regression model has been fitted with the help of dummy variables. Dummy variables can point out the difference if they exist. Here, the base categories are traditional residential area and low income group.
The model can be expressed as follows-
i m n i h n i m c i h c i m i h i n i c i
i a b D b D b D b D b D D b D D b D D b D D u
Y = + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 +
………… (4.2) Where
Yi = factor score vector of the ith factor.
Dc =1, if it is commercial area = 0, otherwise
Dn=1, if newly established residential area =0, otherwise
Dh=1, if high income group =0, otherwise
Dm=1, if middle income group =0, otherwise
DcDh=1, if high income group respondents in commercial area =0, otherwise
DcDm=1, if middle income group in the commercial area
=0, otherwise
DnDh=1, if high income group in newly established residential area =0, otherwise
DnDm=1, if middle income group in newly established residential area =0, otherwise
Ui=error terms
Here, the number of equations would be equal to number of significant factors which affect QOL. Based on above mentioned techniques results have been derived and these results have been discussed in the next chapter.
CHAPTER 5
Quality of life and environment
Literature review reveals that QOL in general intends to refer either to the condition of living environment or to some attribute of people themselves and sometimes to their psychological well-being or the extent to which needs are fulfilled. The quality of living environment in urban environment for the people of the world has emerged as an issue of fundamental concern for academic researchers, policy makers and citizens for the first time in the history of humanity. Therefore, in this study QOL has been appraised in urban living environment for the reason that the degraded living environments in cities of the developing countries may pose a serious threat to the very survival of mankind (Pacione, 2003b).