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CPS2119 Noor Azlin M. S. et al.
            explanatory variables is described through c-1 logits denoted as g_1 (Χ),g_2
            (Χ),…,g_(c-1)  (Χ),  which  relate  a  set  of  intercepts  (α_s)  and  regression
            coefficients (β_s) to the probability of the response levels. The [exp (β_s)] is
            interpreted as the odds ratio for a one-unit increase in the given explanatory
            variable, which is a measure used for comparing two response levels or two
            sets of response levels.
                In  particular,  there  is  no  clear-cut  procedure  on  how  to  choose  the
            appropriate link-function to analyse the ordinal regression model (Christensen
            2015). Accordingly, the main objective of this study is to employ the ordinal
            regression model with different link functions for modelling the relationship
            between  level  of  family  well-being  and  demographic,  socioeconomic  and
            social factors. The four link functions that are considered for this analysis, are
            as given in Table 1.
                                TABLE 1.  Summary of various link functions
                        Function             Distribution        Link Function
                          Logit                Logistic             Log (    )
                                                                        1−
                          Probit               Normal                 −1 ()

                  Complementary log-log     Gumble (min)        Log[− Log (1 − )]
                     Negative log-log       Gumbel (max)         -Log[− Log ( )]

            3.  Application
                The  data  for  this  study  is  obtained  from  the  Family  Well-Being  Index
            Survey, which had been carried out by the National Population and Family
            Development Board of Malaysia in 2011. It consists of information on 2,808
            households which contains some details on family well-being, demographic,
            socioeconomic, and social characteristics. The selection criteria of households
            were  parents  with  child  age  at  least  13  years  old.      The  study  involved  a
            stratified  random  sampling  design  where  the  samples  were  selected
            throughout Malaysia according to strata (urban and rural) and three ethnic
            groups in Malaysia (Bumiputra, Chinese and Indian). For this study, the sample
            of either father or mother interviewed in each household involves the fraction
            of 1,484 fathers (52.8%) and 1,324 mothers (47.2%).
                The response variable (Y) for the ordinal regression model under study is
            expressed as the Level of Satisfaction of Family Well-Being. Respondents were
            asked on overall satisfaction level of their family well-being. The question was
            measured on a 3-point scale (low, moderate, and high). There are two domains
            of explanatory variables for the study that is socio demographic and social
            characteristics. The socio demographic variables consist of Strata (urban/rural),
            Ethnicity (Bumiputra, Chinese and Indian), Type of Family (Nuclear, Blended,
            Single and Extended), Level of Education (Primary, Secondary, Tertiary and No

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