Abstract
Ordinal logistic regression models are used to predict the dependent variable, when dependent variable is of ordinal type in both the situation for single level and multilevel. The most used model for ordinal regression is the Proportional Odd (PO) model which assumes that the effect of the each predictor remains same for each category of the response variable. To estimate the wealth index of household in the province Punjab the proportional odds model is used. The wealth index is an order categorical dependent variable having five categories. The data MICS (2014), a multiple indicator cluster survey conduct by Punjab bureau of statistics was used in this article. The data was recorded at different level such as individual level (household level), district level and division level. The secondary data MICS contains a sample of 41413 household collected from both rural and urban areas of the province Punjab. In the present study analysis were made for single level (household level) and two levels (division level). After fitting the proportional odds model for the single level the proportionality assumption is tested by the brand test whose results suggest that all the predictors fulfill assumption of proportional odds. The significance value suggests that all the predictors have significant effect on the wealth index. The variation due to division level was estimated by two level ordinal logistic regression equal to 5.842, and the Intra Class Correlation ICC is equal to 0.6397 which show that 63.97% of total variation is due to division level.
Highlights
Discrete choice models is a class of model in which the response variable Y takes the counted values such as 0, 1, 2, and so on to a finite number of values (Joe, 2008)
The above proportional odds model gives the cumulative probability j of category j and for the response variable having categories C we find the C 1 cumulative probabilities as for the last category the cumulative probability is always equal to one
As households are nested in the high level of hierarchy such as households are nested in division so we need to fit a two level multilevel ordinal logit model to estimate the response variable wealth index quintile
Summary
Discrete choice models is a class of model in which the response variable Y takes the counted values such as 0, 1, 2, and so on to a finite number of values (Joe, 2008). In the case where the natural ordering exist in the dependent variable. For example the grade of a high school student may, very good, good, satisfactory, poor, and very poor. Another example opinion about a product of soap may be strongly opposed, opposed, neutral, support and strongly support for such a categorically we can code the 1 for" strongly opposed", 2 for "opposed", 3 for "neutral", 4 for " support" and 5 for "strongly support". The values are not quantitative but a natural ordering exist between the values. For the prediction of an ordinal response variable ordinal logistic regression is used (Bello et al, 2016; Christensen, 2010)
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