Quasi-binomial zero-inflated regression model suitable for variables with bounded support

In recent years, a variety of regression models, including zero-inflated and hurdle versions, have been proposed to explain the case of a dependent variable with respect to exogenous covariates. Apart from the classical Poisson, negative binomial and generalised Poisson distributions, many proposals have appeared in the statistical literature, perhaps in response to the new possibilities offered by advanced software that now enables researchers to implement numerous special functions in a relatively simple way. However, we believe that a significant research gap remains, since very little attention has been paid to the quasi-binomial distribution, which was first proposed over fifty years ago. We believe this distribution might constitute a valid alternative to existing regression models, in situations in which the variable has bounded support. Therefore, in this paper we present a zero-inflated regression model based on the quasi-binomial distribution, taking into account the moments and maximum likelihood estimators, and perform a score test to compare the zero-inflated quasi-binomial distribution with the zero-inflated binomial distribution, and the zero-inflated model with the homogeneous model (the model in which covariates are not considered). This analysis is illustrated with two data sets that are well known in the statistical literature and which contain a large number of zeros.     

Applications and Implementation DECISION SUPPORT SYSTEMS: AN EMPIRICAL ASSESSMENT FOR DECISION MAKING

A laboratory experiment examined the effects of applying decision support system (DSS) technology to decision making in ill-structured problem environments under varying information conditions. Marketing executives participated in the experiment which investigated the effects of DSS availability, DSS training, and data availability on dependent variables that included: (1) the number of alternatives considered by a subject during decision making, (2) the period of time spent by a subject to complete the decision-making process, (3) the subject's perceived confidence in the decisions he or she had made, (4) the amount of data considered by a subject's during decision making, (5) the individual subject's decision processing, and (6) the subject's performance overall. Our results indicate that all three factors significantly affect the number of alternatives considered by subjects during the decision-making process. We therefore suggest that DSS training be coordinated with decision training in order to realize the potential of DSSs as described in the DSS literature.     

ON MODELING ADVERTISING PULSING DECISIONS

Based on empirical findings in the literature, sales response to advertising pulsing policy (APP) is modeled mathematically. The implications for APP are discussed. This policy is compared with an alternative policy of uniform expenditures (UAP), a commonly used strategy. The results of the research indicate that substantial savings in advertising budget or an increase in sales revenues may be achieved for a firm using APP.     

AD HOC MODEL BUILDING USING TIME-VARYING PARAMETER MODELS*

Decision support for managers and policy makers, such as required in planning and evaluation efforts, often requires ad hoc behavioral modeling to account for context-specific phenomena and to handle data limitations. This paper introduces a systematic approach useful for meeting these requirements in which time-varying parameter estimation plays an important role. A case study evaluating the impacts of public policy actions on residential natural gas conservation illustrates the approach.     

How do marital status,work effort,and wage rates interact?

How marital status interacts with men's earnings is an important analytic and policy issue, especially in the context of debates in the United States over programs that encourage healthy marriage. This paper generates new findings about the earnings-marriage relationship by estimating the linkages among flows into and out of marriage, work effort, and wage rates. The estimates are based on National Longitudinal Survey of Youth panel data, covering 23 years of marital and labor market outcomes, and control for unobserved heterogeneity. We estimate marriage effects on hours worked (our proxy for work effort) and on wage rates for all men and for black and low-skilled men separately. The estimates reveal that entering marriage raises hours worked quickly and substantially but that marriage's effect on wage rates takes place more slowly while men continue in marriage. Together; the stimulus to hours worked and wage rates generates an 18%-19% increase in earnings, with about one-third to one-half of the marriage earnings premium attributable to higher work effort. At the same time, higher wage rates and hours worked encourage men to marry and to stay married. Thus, being married and having high earnings reinforce each other over time.     

On the minimum expected quantity for the validity of the chi-squared test in 2 2 2 tables

A 2 2 2 contingency table can often be analysed in an exact fashion by using Fisher's exact test and in an approximate fashion by using the chi-squared test with Yates' continuity correction, and it is traditionally held that the approximation is valid when the minimum expected quantity E is E S 5. Unfortunately, little research has been carried out into this belief, other than that it is necessary to establish a bound E>E*, that the condition E S 5 may not be the most appropriate (Martín Andrés et al., 1992) and that E* is not a constant, but usually increasing with the growth of the sample size (Martín Andrés & Herranz Tejedor, 1997). In this paper, the authors conduct a theoretical experimental study from which they ascertain that E* value (which is very variable and frequently quite a lot greater than 5) is strongly related to the magnitude of the skewness of the underlying hypergeometric distribution, and that bounding the skewness is equivalent to bounding E (which is the best control procedure). The study enables estimating the expression for the above-mentioned E* (which in turn depends on the number of tails in the test, the alpha error used, the total sample size, and the minimum marginal imbalance) to be estimated. Also the authors show that E* increases generally with the sample size and with the marginal imbalance, although it does reach a maximum. Some general and very conservative validity conditions are E S 35.53 (one-tailed test) and E S 7.45 (two-tailed test) for alpha nominal errors in 1% h f h 10%. The traditional condition E S 5 is only valid when the samples are small and one of the marginals is very balanced; alternatively, the condition E S 5.5 is valid for small samples or a very balanced marginal. Finally, it is proved that the chi-squared test is always valid in tables where both marginals are balanced, and that the maximum skewness permitted is related to the maximum value of the bound E*, to its value for tables with at least one balanced marginal and to the minimum value that those marginals must have (in non-balanced tables) for the chi-squared test to be valid.     

Binary probability maps using a hidden conditional autoregressive Gaussian process with an application to Finnish common toad data

The Finnish common toad data of Heikkinen and Hogmander are reanalysed using an alternative fully Bayesian model that does not require a pseudolikelihood approximation and an alternative prior distribution for the true presence or absence status of toads in each 10 km×10 km square. Markov chain Monte Carlo methods are used to obtain posterior probability estimates of the square-specific presences of the common toad and these are presented as a map. The results are different from those of Heikkinen and Hogmander and we offer an explanation in terms of the prior used for square-specific presence of the toads. We suggest that our approach is more faithful to the data and avoids unnecessary confounding of effects. We demonstrate how to extend our model efficiently with square-specific covariates and illustrate this by introducing deterministic spatial changes.     

Decision Making in `Random in a Broad Sense' Environments

It is shown that the uncertainty connected with a `random in a broad sense' (not necessarily stochastic) event always has some `statistical regularity' (SR) in the form of a family of finite-additive probability distributions. The specific principle of guaranteed result in decision making is introduced. It is shown that observing this principle of guaranteed result leads to determine the one optimality criterion corresponding to a decision system with a given `statistical regularity'.     

Standard errors for EM estimation

The EM algorithm is a popular method for computing maximum likelihood estimates. One of its drawbacks is that it does not produce standard errors as a by-product. We consider obtaining standard errors by numerical differentiation. Two approaches are considered. The first differentiates the Fisher score vector to yield the Hessian of the log-likelihood. The second differentiates the EM operator and uses an identity that relates its derivative to the Hessian of the log-likelihood. The well-known SEM algorithm uses the second approach. We consider three additional algorithms: one that uses the first approach and two that use the second. We evaluate the complexity and precision of these three and the SEM in algorithm seven examples. The first is a single-parameter example used to give insight. The others are three examples in each of two areas of EM application: Poisson mixture models and the estimation of covariance from incomplete data. The examples show that there are algorithms that are much simpler and more accurate than the SEM algorithm. Hopefully their simplicity will increase the availability of standard error estimates in EM applications. It is shown that, as previously conjectured, a symmetry diagnostic can accurately estimate errors arising from numerical differentiation. Some issues related to the speed of the EM algorithm and algorithms that differentiate the EM operator are identified.     

Using Experiential Learning to Help Students Understand the Impact of Food Insecurity

Experiential learning theory suggests that students increase their understanding when given the opportunity to experience a particular situation in addition to learning about it intellectually. This theory was used to construct an assignment to assist social work master’s students in better understanding food insecurity and the Supplemental Nutrition Assistance Program (SNAP). Through coding previously collected reactions to the assignment, the researchers discovered multiple reoccurring themes: increased understanding of SNAP, feelings about the program, realizations regarding individual privilege, client stigma, the social experience of eating, and empathy for those who experience food insecurity. Through this exercise, students increased their knowledge of the program and also gained a better understanding of how food insecurity personally affects individuals and families.