Comparative Statics,Informativeness, and the Interval Dominance Order

We identify a new way to order functions, called the interval dominance order, that generalizes both the single crossing property and a standard condition used in statistical decision theory. This allows us to provide a unified treatment of the major theorems on monotone comparative statics with and without uncertainty, the comparison of signal informativeness, and a non‐Bayesian theorem on the completeness of increasing decision rules. We illustrate the concept and results with various applications, including an application to optimal stopping time problems where the single crossing property is typically violated.     

Learning While Voting: Determinants of Collective Experimentation

This paper combines dynamic social choice and strategic experimentation to study the following question: How does a society, a committee, or, more generally, a group of individuals with potentially heterogeneous preferences, experiment with new opportunities? Each voter recognizes that, during experimentation, other voters also learn about their preferences. As a result, pivotal voters today are biased against experimentation because it reduces their likelihood of remaining pivotal. This phenomenon reduces equilibrium experimentation below the socially efficient level, and may even result in a negative option value of experimentation. However, one can restore efficiency by designing a voting rule that depends deterministically on time. Another main result is that even when payoffs of a reform are independently distributed across the population, good news about any individual's payoff increases other individuals' incentives to experiment with that reform, due to a positive voting externality.     

Influence Measures in Quantile Regression Models

In this article, we use the asymmetric Laplace distribution to define a new method to determine the influence of a certain observation in the fit of quantile regression models. Our measure is based on the likelihood displacement function and we propose two types of measures in order to determine influential observations in a set of conditional quantiles conjointly or in each conditional quantile of interest. We verify the validity of our average measure in a simulated data set as well in an illustrative example with data about air pollution.     

Sample Heterogeneity and the Measurement Structure of the Multidimensional Students’ Life Satisfaction Scale

Several measurement assumptions were examined with the goal of assessing the validity of the Multidimensional Students’ Life Satisfaction Scale (MSLSS), a measure of adolescents’ satisfaction with their family, friends, living environment, school, self, and general quality of life. The data were obtained via a cross-sectional survey of 8,225 adolescents in British Columbia, Canada. Confirmatory factor and factor mixture analyses of ordinal data were used to examine the measurement assumptions. The adolescents did not respond to all the MSLSS items in a psychometrically equivalent manner. A correlated five-factor model for an abridged version of the MSLSS resulted in good fit when all negatively worded items and several positively worded items (the least invariant) were excluded. The abridged 18-item version of the MSLSS provides a promising alternative for the measurement of five life domains that are pertinent to adolescents’ quality of life.     

Multiple-Indicator Multilevel Growth Model: A Solution to Multiple Methodological Challenges in Longitudinal Studies

This paper described the versatility of the multiple-indicator multilevel (MIML) model in helping to resolve four common challenges in studying growth using longitudinal data. These challenges are (1) how to deal with changes in measurement over time and investigate temporal measurement invariance, (2) how to model residual dependence due to the nested nature of longitudinal data, (3) how to model observed trajectories that do not follow well-known functions commonly discussed in the methodology literature (e.g., a linear or quadratic curve), and (4) how to decide which predictors are relatively more important in explaining individuals’ change over time. With an example of psychological well-being from the Wisconsin Longitudinal Study, we illustrated how the four methodological challenges can be resolved using the 3-phase MIML procedures and the Pratt’s importance measures.     

Certificates of optimality: the third way to biproportional apportionment

The biproportional apportionment problem (BAP) must be faced in many proportional electoral systems where seats must be allocated to parties within regions. BAP is a non-trivial optimization problem, and only sophisticated algorithms are currently available for solving it. The issue is: are they “writable” as an actual law? Citizens rightly demand simple, easy to understand, voting systems. The alternative, though, seems to have simple, but unsound electoral laws. We propose the following way out of this dilemma: leave to a mathematically sophisticated algorithm the task of producing an optimal apportionment, but attach to it a “certificate of optimality”, that is, describe a simple procedure whereby anybody can check, through some elementary operations, that the seat allocation output by the algorithm is indeed an optimal apportionment. We discuss one such certificate, based on the Max flow- min cut Theorem, relative to a parametric max flow method of ours for BAP.     

A spatiotemporal model for Mexico City ozone levels

Summary.  We consider hourly readings of concentrations of ozone over Mexico City and propose a model for spatial as well as temporal interpolation and prediction. The model is based on a time-varying regression of the observed readings on air temperature. Such a regression requires interpolated values of temperature at locations and times where readings are not available. These are obtained from a time-varying spatiotemporal model that is coupled to the model for the ozone readings. Two location-dependent harmonic components are added to account for the main periodicities that ozone presents during a given day and that are not explained through the covariate. The model incorporates spatial covariance structure for the observations and the parameters that define the harmonic components. Using the dynamic linear model framework, we show how to compute smoothed means and predictive values for ozone. We illustrate the methodology on data from September 1997.     

Dynamic models for spatiotemporal data

We propose a model for non-stationary spatiotemporal data. To account for spatial variability, we model the mean function at each time period as a locally weighted mixture of linear regressions. To incorporate temporal variation, we allow the regression coefficients to change through time. The model is cast in a Gaussian state space framework, which allows us to include temporal components such as trends, seasonal effects and autoregressions, and permits a fast implementation and full probabilistic inference for the parameters, interpolations and forecasts. To illustrate the model, we apply it to two large environmental data sets: tropical rainfall levels and Atlantic Ocean temperatures.     

The choice of time interval in seasonal adjustment: A heuristic approach

A typical problem of the seasonal adjustment procedures arises when the series to be adjusted is subject to structural breaks. In fact, using the full span of the series can result in a biased estimation of the “true” seasonally adjusted series, with unclear evidence showed by the usual diagnostic tests. In these cases the researcher has to decide where to cut-off the observed series to obtain a homogeneous span; this is generally performed by a simple visual inspection of the graph of the series and/or using a-priori information about the occurrence of the break. In this paper we propose a statistical criterion based on a distance measure between filters, evaluating its performance with Monte Carlo experiments. The first results of this work have been presented at the XL scientific meeting of the Italian statistical society, Florence, 26–28 April 2000, benefiting of the discussion arisen there; a preliminary version of this paper circulated as ISAE working paper No. 21/2001 with the title “The Choice of Time Interval in Seasonal Adjustment: Characterization and Tools”. We thank an anonymous referee for precious suggestions. The authors are solely responsible of any remaining error.