The study presents the results of a survey experiment aimed at assessing the level of life satisfaction for rural north Indians and captures the determinants in deciding one’s satisfaction level. The study hypothesised human, material and social capital plays a significant role in determining one’s level of life satisfaction. The study uses individual data from the Sanitation Quality, Use, Access and Trends (SQUAT) survey collected in rural Bihar, Haryana, Madhya Pradesh, Rajasthan, and Uttar Pradesh in 2013–14 from India. The study estimates first, proportional odds logistic regression, followed by Generalised Ordinal Logistic regression techniques. It is evident from the analysis that the overall PO assumption, as well as separate PO assumptions for most of the variables, is violated and, in that case, generalised ordinal logistic regression may provide a better model. From the analysis, it is very clear that for rural north Indians the level of life satisfaction is most affected by health status, possession of agricultural land,and administrative environment of villages (e.g., functioning of Panchayats).

Earlier reviews showed that there is a dearth of literature on life satisfaction when it comes to Asian countries, particularly the developing and less developed countries from Asia. I found very few studies from India and even that were only related to limited factors influencing life satisfaction. The present study tries to measure the level of life satisfaction for rural north Indians and capture the determinants in deciding one’s satisfaction level. The study hypothesised that whether human, material and social capital play a significant role in determining one’s level of life satisfaction and for testing the same on econometric tools the study presents the methodology and conceptual framework in subsequent sections.

The present study uses individual data from the Sanitation Quality, Use, Access and Trends (SQUAT) survey collected in rural Bihar, Haryana, Madhya Pradesh, Rajasthan, and Uttar Pradesh in 2013–14 by a team of researchers. These data and their representative sampling strategy have previously been described in detail in ^{1}. The SQUAT survey was a multipurpose survey with hourlong interviews on a range of topics. Therefore, neither the occupational nor caste-related questions could directly influence the asset count measure (

The data set and questionnaires are available at

The study uses various variables which are described by variable type, description,and corresponding range (see

Description of variables used in the study

The outcome variable is the life satisfaction level of rural north Indian individuals, which is an ordinal variable with three levels (1 = low life satisfaction; 2 = medium life satisfaction and 3 = high life satisfaction level). These three levels of satisfaction were upward ordinal structured and

As our dependent variable is ordinal of categories then conventional ordinary least square (OLS) regression techniques are inappropriate because OLS regression is only useful when the dependent variable is continuous. In such cases where the dependent variable is ordinal of categories of more than two, the proportional odds model or ordered logit regression is a better alternative. However, in cases, the assumption of proportional odds or parallel lines is violated; the generalised ordinal logit regression is a superior alternative because it is less restrictive than earlier methods and more parsimonious than methods like multinomial logit regression which does not consider the ordinal nature of regressand.

The PO model estimates the cumulative probability of being at or below a particular level of the dependent variable or being beyond that level. The interpretation of predictors in this model is according to the assumption of proportional odds or parallel line which assumes the effect of each predictor is to be the same across the categories of the ordinal regressand, meaning thereby, for each regressor, the effect on the likelihood of being at or below any level/category does not change within the model.

The binary logistic regression analysis, as we know, should have a dichotomous dependent variable. As far as the regressand is categorical, we cannot predict ordinary least square (OLS) estimates because the bestfit approach is based on minimizing error term and this is inappropriate in the case of categorical regressand. For that purpose, binomial probability theory is applied in logistic regression which predicts only two values: that probability (p) is 1 or 0, i.e. the event/person belongs to one group or the other.

The logistic regression model can be defined as:

But as the study encounters regressand that is of more than two categories as well as ordinal, the ordinal logistic regression estimated the odds of being at or below a specific outcome level given some regressors. The aforementioned model can be expressed in the following form as follows:

Where _{j} are cut points which usually indicates where the regressand is cut to make three categories that I observe in data. In general, the cut-points are closely related to thresholds and β_{1}, β_{2}, β_{3}, … β_{n} are logit coefficients. This PO model estimates J – 1 cut points and according to PO or parallel line assumption, it assumes the coefficients for the underlying binary models are the same across all cut points.

To estimate the likelihoods of being at or below the ^{th} category, the PO model can be extended as follows:

Most of the time the PO assumption is violated for some or the other regressors and I have to go for postestimation tests like the Brant test to testify whether the PO assumption is met for some or the other regressors or not. The Brant test estimates logistic coefficients for underlying binary logistic regression and produces the chi-square test statistics for each regressor and the overall model.

The GOLOGIT model is an extension or improvement over the PO model. Whenever the PO assumption is violated for some or the other predictor variables, the PO estimations are not correct or more appropriately say not correctly specified. The Brant test, which is used to testify the PO assumption, specifies which regressors are violating the PO assumption, and if the assumption is violated by certain regressors, then the GOLOGIT model estimates the odds freely across different levels/ categories of the regressand. The model can be expressed as follows:

The above form can also be rewritten as follows:

Where _{j}_{1j}, β_{2j}, β_{3j}, …, β_{nj} are logistic coefficients. This model estimates the likelihood of being beyond a certain level/category relative to being at or below that level/category. A positive logit coefficient indicates that the likelihood of being in a higher level/category is more for an individual/event than to a lower level/category of the regressand and vice versa. To estimate the likelihoods of being at or below a particular level/category, however, the signs must be reversed before both the intercepts and logit coefficients in equation (

A special case of the GOLOGIT model is the Partial Proportional Odds (PPO) model, which allows for interactions between a regressor that violates the PO assumption and different levels/categories of the ordinal regressand. On the other hand, the GOLOGIT model relaxes the PO assumption for each regressor to vary across different cut-points of the ordinal regressand i.e. this model estimates parameters that are different from the PPO model.

First, the Proportional Odds (PO) model uses the life satisfaction level as our regressand and human capital, material capital, and social capital as our regressors to estimate the level of life satisfaction among rural north Indians. The study controls for gender and state variables to capture the regional differences in life satisfaction levels of individuals. The human capital variables include age, years of education and health perspective of individuals, material capital includes the main source of livelihood (main occupation), possession of agricultural land and asset count and lastly; social capital includes the social category, heterogeneity of castes in villages, peaceful environment and functioning of the panchayat. The equation for PO logistic regression can be given as follows:

Where there are

The variable on the left-hand side (L.H.S) level of life satisfaction is ordinal of three categories and taken as regressand.

The variables on the right-hand side (R.H.S.) are the regressors of the model and are the error term and residuals.

The PO model for these three different capitals has been fitted as Model 1 including only human capital, Model 2 including both human and material capital, and Model 3 including all three types of capital e.g. human, material and social.

The Brant test was then used as the analysis of the post-estimation test to examine the PO assumption (parallel line assumption) and identify regressors that violated the assumption. After that, based on Brant test diagnostic the study uses the generalised ordinal logit model or PPO model to correctly specify our model of estimation of life satisfaction level on the same equation one (equation

For the year 2013-14 outcome variable; life satisfaction level, which is an ordinal variable with three levels (low, medium, and high) showed the hierarchical structure as category high indicates higher levels of all previous levels.

Life satisfaction categories and proportions for sample SQUAT 2013-14

A PO model for human capital was fitted first (Model 1) and subsequently, the models for material (Model 2) and social capital (Model 3) were estimated. The overall model fit for Model 1, = 3739.97, p <0.01, indicates that the coefficient of the regressors was statistically significantly different from 0 (see

The odds (>1) for human capital indicated that the likelihood of being at or below a particular level of satisfaction relative to beyond that level increases as a unit increase in human capital indicators. In other words, a higher level of human capital, particularly the health of an individual, was related to the likelihood of being in a higher level of life satisfaction.

Model 2 which was fitted with human and material capital showed the model gets better with material capital and the log-likelihood ratio or Pseudo ^{th}^{th} = 4563.55, p <0.01 (see

Results of the proportional odds model (ordinal logistic regression)

After including the variables for material capital e.g. labour market status, possession of agricultural land, and asset count, human capital variables like; age and education became insignificant but still, the variable of health status was significantly affecting life satisfaction level which again proves the importance of better health in deciding life satisfaction for rural north Indians. The logit regression coefficients for material capital showed that better employment or labour market status, possession of agricultural land, and increased asset count was related to the likelihood of being at a higher level of life satisfaction. It is evident from the regression coefficients and odds of material capital that it is positively significantly related to life satisfaction level, particularly being in self-employment and possession of agricultural land in rural north India was highly significant and positively related to an increased likelihood of being in the higher level of life satisfaction.

Our full PO Model (model 3) that is for human, material, and social capital has a better fit and the loglikelihood ratio or Pseudo ^{rd}

The full model also estimated five cut points, which were used to differentiate among adjoining categories of level of life satisfaction. Here and were the cut points for a logistic model for Y > 1 and Y > 2 respectively.

Brant tests of the proportional odds (PO) assumption for each predictor and the overall model

The Brant test is used to identify whether the overall model/separate variables (each predictor) follow the PO assumption or not. _{12}^{2}= 370.47, p = 0.000, points out that the PO assumption for the overall model gets violated (see

The generalised ordinal model estimates the logistic coefficients and corresponding odds ratios for all regressors at different levels/categories e.g. beyond one level versus at or below that level. The outcome variable (e.g. life satisfaction level) has three categories so in the PPO model, I have two categories to be compared. After relaxing the PO assumption, the model fit gets better and LR ^{2}

Results of Partial Proportional Odds Model (Generalised Ordinal Logit)

The effects of material capital like possession of agricultural land and asset count were also positively associated with the likelihood of being above a particular level of life satisfaction as opposed to being at or below that level. It is clear from the odds that the effects of material capital became weaker when life satisfaction level moved from low to high. Among social capital the effect of a peaceful environment of the village was first negative and further became positive with lower to a higher level of life satisfaction, moreover; better functioning of Panchayats in villages was associated with the likelihood of being in a higher level of life satisfaction and the effect became much stronger when satisfaction level moved from low to high.

To analyse the determinants of life satisfaction level for rural north Indians, the study estimated first, proportional odds logistic regression, followed by generalised ordinal logistic regression techniques. It is evident from the analysis that the overall PO assumption, as well as separate PO assumptions for most of the variables, is violated and, in that case, generalised ordinal logistic regression may provide a better model. From the analysis, it is very clear that for rural north Indians the level of life satisfaction is most affected by health status, possession of agricultural land, and administrative environment of villages (e.g. functioning of Panchayats). Better health, possession of agricultural land, and better functioning of Panchayats significantly affect the life satisfaction level of rural north Indians after controlling for gender and regional differences. The effects of other capitals like better occupation, increased assets, heterogeneity of castes, and peaceful environment are also significant except age and education of an individual in rural north India. Our results got support from previous studies like

The results indicate policy implications in advancing health facilities in rural India. This is only a part of good governance and the overall functioning of local governance can be made more transparent which was most significant in deciding life satisfaction because individuals or society expect so much from an elected government in a democracy. Besides, agricultural land being a resource in rural India affects life satisfaction very significantly. Particularly for those who do not possess agricultural land and mainly for the socially deprived sections of society, the policy of land reforms is most important. Why education is not significant in deciding life satisfaction for rural north Indians can be interpreted as very low educational outcome and occupational opportunities in rural India. The implications may be limiting as the sample consists of only five states from rural India and I may get more precise estimations using a larger sample size consisting of all the rural settlements of India. This also helps to get some potential directions for future studies to have a larger sample size and include some other psychological aspects relating to life satisfaction which may be done with an interdisciplinary approach.

The views expressed in this paper are those of the author and do not reflect the views of the institution to which the author is affiliated. I thank my colleagues who provided insights and expertise which greatly assisted the research, although any errors are my own and should not tarnish the reputation of esteemed persons from respective institutions.