Causality and interdependence analysis in linear econometric models with an application to fertility

This paper is an applied analysis of the causal structure of linear multi-equational econometric models. Its aim is to identify the kind of relationships linking the endogenous variables of the model, distinguishing between causal links and feedback loops. The investigation is first carried out within a deterministic framework and then moves on to show how the results may change inside a more realistic stochastic context. The causal analysis is then specifically applied to a linear simultaneous equation model explaining fertility rates. The analysis is carried out by means of a specific RATS programming code designed to show the specific nature of the relationships within the model.     

EXACT INFERENCE IN FOUR-PARAMETER GENERALIZED GAMMA DISTRIBUTIONS

The paper considers Bayesian analysis of the generalized four-parameter gamma distribution. Estimation of parameters using classical techniques is associated with important technical problems while Bayesian methods are not currently available for such distributions. Posterior inference is performed using numerical methods organized around Gibbs sampling. Predictive distributions and reliability can be estimated routinely using the proposed methods.     

The local geographies of welfare in Tunisia: Does neighbourhood matter?*

Amara M, Ayadi M. The local geographies of welfare in Tunisia: Does neighbourhood matter? The aim of this article is to show that spatial analysis techniques outperform non‐spatial statistical counterparts for understanding the geographic determinants of welfare and poverty in Tunisia. First, an Exploratory Spatial Data Analysis, based on a Geographical Information System, was conducted to visualise the local spatial structure of welfare. Second, a spatial autoregressive (SAR) model and a geographically weighted regression (GWR) model, respectively, were used to deal with both spatial autocorrelations and unobserved spatial heterogeneity of households' behaviours. Spatial and non‐spatial models were compared according to their predictive performances. Results of this case study confirm that SAR and GWR spatial models are preferable to the traditional non‐spatial regression model and that they give a better approximation of the Tunisian poverty map.     

Some Correlates of Emotional Well-Being Among New England College Students

Abstract

In a questionnaire survey of New England college students, a large number of undergraduate men and women reported problems related to their personal, social, or academic adjustment. Given a list of 22 items described as “common concerns or feelings experienced by college students,” respondents were asked to rate the extent to which each item had been a problem for them in the past year. Most students (86%) reported having very much or somewhat of a problem with one or more items on the list. Pressure to do well in school, problems with weight control, anxiety, poor concentration and depression were among the most commonly reported concerns. The prevalence of these self-reported concerns and problems was found to be significantly associated with the respondents' sex, their perceptions of their health status, and academic standing.     

Outlier detection by robust principal components analysis

The robust principal components analysis (RPCA) introduced by Campbell (Applied Statistics 1980, 29, 231–237) provides in addition to robust versions of the usual output of a principal components analysis, weights for the contribution of each point to the robust estimation of each component. Low weights may thus be used to indicate outliers. The present simulation study provides critical values for testing the kth smallest weight in the RPCA of a sample of n p-dimensional vectors, under the null hypothesis of a multivariate normal distribution. The cases p=2(2)10, 15, 20 for n=20, 30, 40, 50, 75, 100 subject to n≥p/2, are examined, with k≤√n.     

MODELING THE LIFETIME OF LONGITUDINAL ELEMENTS

In the study of the stochastic behaviour of the lifetime of an element as a function of its length, it is often observed that the failure time (or lifetime) decreases as the length increases. In probabilistic terms, such an idea can be expressed as follows. Let T be the lifetime of a specimen of length x, so the survival function, which denotes the probability that an element of length x survives till time t, will be given by S_T (t, x) = P(T > t/α(x), where α(x) is a monotonically decreasing function. In particular, it is often assumed that T has a Weibull distribution. In this paper, we propose a generalization of this Weibull model by assuming that the distribution of T is Generalized gamma (GG). Since the GG model contains the Weibull, Gamma and Lognormal models as special and limiting cases, a GG regression model is an appropriate tool for describing the size effect on the lifetime and for selecting among the embedded models. Maximum likelihood estimates are obtained for the GG regression model with α(x) = cx^b . As a special case this provide an alternative to the usual approach to estimation for the GG distribution which involves reparametrization. Related parametric inference issues are addressed and illustrated using two experimental data sets. Some discussion of censored data is also provided.     

Is categorization of random data necessary for parallel analysis on Likert-type data?

Random eigenvalues are the key elements in parallel analysis. When analyzing Likert-type data, is it necessary to convert the continuous random data to discrete type before estimating eigenvalues? The study compared the random eigenvalues obtained from continuous and categorized random data from two popular computer programs to be used as the basis for comparison in conducting parallel analysis on Likert-type data. Results indicated that categorized random data gave eigenvalues and number of factors similar to those obtained from continuous random data. It is suggested that when conducting parallel analysis on Likert-type data by the two programs, the conversion is unnecessary.     

Deciding with Thresholds: Importance Measures and Value of Information

Risk‐informed decision making is often accompanied by the specification of an acceptable level of risk. Such target level is compared against the value of a risk metric, usually computed through a probabilistic safety assessment model, to decide about the acceptability of a given design, the launch of a space mission, etc. Importance measures complement the decision process with information about the risk/safety significance of events. However, importance measures do not tell us whether the occurrence of an event can change the overarching decision. By linking value of information and importance measures for probabilistic risk assessment models, this work obtains a value‐of‐information‐based importance measure that brings together the risk metric, risk importance measures, and the risk threshold in one expression. The new importance measure does not impose additional computational burden because it can be calculated from our knowledge of the risk achievement and risk reduction worth, and complements the insights delivered by these importance measures. Several properties are discussed, including the joint decision worth of basic event groups. The application to the large loss of coolant accident sequence of the Advanced Test Reactor helps us in illustrating the risk analysis insights.     

Regression for non-Euclidean data using distance matrices

Regression methods for common data types such as measured, count and categorical variables are well understood but increasingly statisticians need ways to model relationships between variable types such as shapes, curves, trees, correlation matrices and images that do not fit into the standard framework. Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which requires only the specification of a distance function. A low-dimensional representation of such distance matrices can be obtained using methods such as multidimensional scaling. Once these variables have been represented as scores, an internal model linking the predictors and the responses can be developed using standard methods. We call scoring as the transformation from a new observation to a score, whereas backscoring is a method to represent a score as an observation in the data space. Both methods are essential for prediction and explanation. We illustrate the methodology for shape data, unregistered curve data and correlation matrices using motion capture data from an experiment to study the motion of children with cleft lip.