استفاده از مدل رگرسیون لجستیک ترتیبی برای تحلیل طبقات مصرف برق خانگی در ریو دو ژانیرو، برزیل

This study applies the proportional odds and partial proportional odds models for ordinal logistic regression to analyze household electricity consumption classes. Micro-data from households situated in the state of Rio de Janeiro during 2004 was used to measure the performance of the models in correctly classifying household electricity consumption classes via sociodemographic, electricity usage and dwelling characteristics. The strategy of using binary logistic regressions to test the main hypothesis of the proportional odds model, suggested by Bender and Grouven, was successful in identifying which of the independent variables could be estimated via the proportional odds assumption. Results indicate that the partial proportional odds models is slightly superior to the more restrictive approach. The study includes probabilistic examples to describe how changes in the independent variables affect the probability of a household belonging to specific classes of electricity consumption. Projections using the final model indicated that the approach may be useful for estimating aggregate household electricity consumption.

Micro-data analysis on household electricity demand has generally focused on KWh level consumption (Andersson and Damsgaard, 1999, Halvorsen and Larsen, 1999, Fung et al., 1999 and Westley, 1992), mainly for the estimation of short-run and long-run elasticities. However, when information on electricity consumption is only available in collapsed form (i.e., consumption classes) traditional OLS approach cannot be used due to the discrete nature and limited range of the dependent variable. One option for researchers with restricted information on electricity consumption is to apply ordinal regression techniques. In this case, although elasticity estimation is not possible via ordinal models, probabilistic examples can be used to illustrate the influence of the independent variables on the likelihood of a household belonging to one of the consumptions classes. Moreover, as in Jung (1993), ordinal regression techniques can also be used to estimate aggregate annual household electricity demand. Thus, we argue that researchers with limited information on household electricity consumption can still obtain informative results via this approach. A review of the literature on cross-sectional modeling of household electricity demand indicates only one article which has applied the logistic model in this field (Jung, 1993). This study applies the proportional odds model (POM) and the partial proportional odds model (PPOM) for ordinal logistic regression in order to analyze household electricity consumption classes in the state of Rio de Janeiro, Brazil. The data was obtained from face-to-face interviews with approximately 2000 households during the year of 2004. The questionnaire included modules related to sociodemographic, dwelling characteristics and electricity usage information.2 The objectives of this research are: (i) to find the best models for the three approaches: proportional odds (POM), partial proportional odds (PPOM) and generalized ordered logit; (ii) compare the final models via the likelihood ratio (LR) test, Akaike Information Criteria (AIC), Schwarz's Bayesian Information Criterion (BIC); (iii) test the strategy suggested by Bender and Grouven (1998) to identify which of the independent variables (IVs) can be summarized by a single coefficient (i.e., by means of the proportional odds); (iv) evaluate and compare the performance of the proportional odds and the partial proportional odds models in correctly classifying the households' electricity consumption classes based on their sociodemographic; electricity usage and dwelling related information; (v) describe, via probabilistic examples, how changing the values of the independent variables affect the probabilities of a household belonging to specific electricity consumption classes and (vi) evaluate the performance of the final model in predicting actual annual aggregate household electricity demand. Regarding objective (iv), most statistical softwares provide output which include observed and predicted classification for each observation, thus allowing us to calculate not only the accuracy rate of the entire sample, but also the rate for each consumption class. Lastly, split-sample validation will be implemented to evaluate the stability of the final model.

This study implemented a multivariate ordinal logistic analysis of micro-data regarding household electricity consumption classes in Rio de Janeiro, Brazil. Three ordinal logistic regression models were estimated and compared: the proportional odds model (POM); the partial proportional odds model (PPOM) and the generalized ordered logit (GOLOGIT). Results indicated that the PPOM is the superior model, allowing for the inclusion of a fifth IV (TOT_IND) which had been excluded from the POM due to the variable's rejection of the proportional odds assumption. It should be noted, however, that results indicated that the POM was able to predict household electricity consumption classes correctly 52.87% of the time, i.e., almost as well as the PPOM (54.61%). The latter approach, nonetheless, by including the IV TOT_IND with non-proportional odds, did improve the accuracy rate of the CLASS 2 (from 6.8% to 24.6%). Both models performed well regarding the main consumption electricity class (Class 3), correctly predicting over 83%–86% of the households in this category. Both approaches also performed well in comparison to the proportional-by-chance accuracy rate, but were approximately 3%–5% percentage points below the maximum-by-chance accuracy rate. The use of binary logistic regressions, suggested by Bender and Grouven (1998), was successful in detecting the IVs (INCOME, INDEX, AREA and R_MOVED) which could be estimated via the PO assumption and which IVs required non-proportional odds (TOT_IND). Thus, our study corroborates this strategy, i.e., that “…careful application of separate binary logistic regressions represents a simple and adequate tool to analyze ordinal data with non-proportional odds”. (Bender and Grouven, 1998, p.809) Split-sample cross-validation was implemented and the accuracy rate of the holdout sample (51.65%) was less then 5% smaller than the performance of the training sample (55.54%). Examples were included to describe how the independent variables affect the probability of a household belonging to specific consumption classes. These examples were implemented for various ‘household scenarios’ (e.g., low-income, median and high-income-class households) in order to assess the magnitude of the impact of the IVs for families in distinct socio-economic backgrounds. Lastly, as in Jung (1993), our results indicated that ordinal regression techiques may be able to help household electricity demand researchers in estimating annual aggregate demand.