Tests for time series of counts based on the probability-generating function

We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical probability-generating function computed from the observations. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is included as well as real-data examples.     

Demographic Shifts in the Czech Republic after 1989: A Second Demographic Transition View

A dramatic change in fertility,family formation and living arrangements tookplace in the Czech Republic over the 1990s. Theestablishment of democracy, profound socialtransformation and transition to the marketeconomy affected the values and demographicbehaviour of the young Czech generation. Thispaper examines whether these demographic shiftscan be interpreted within the framework of thesecond demographic transition. The theoreticalpart discusses the idea of the transition,outlining three distinctive conceptualisations.Two of them – the view of the transition as aprogression of characteristic interrelateddemographic changes and a broader viewstressing the importance of underlyingideational factors – fit the Czech situationvery well. A comparison with the Netherlandsreveals that the onset of the transition in theCzech Republic may be clearly located in thefirst half of the 1990s, lagging two decadesbehind the Netherlands.     

Statistical Methods and Graphical Displays for Analyzing How the Association Between Two Qualitative Variables Differs Among Countries, Among Groups, Or Over Time: A Modified Regression-Type Approach

Many interesting sociological questions pertain to how the association between two variables depends on a third variable. In sociological applications, the third variable often pertains to countries, to subgroups of a population, or to time periods. We propose a regression-type approach that specifies that the log-odds- ratios that describe the two-way association of interest are a linear function of latent scores for the third variable. Additive and multiplicative models currently in use by researchers are special cases of the regression-type model. To illustrate the utility of the regression-type approach, we apply this approach to analyze (1) data on occupational mobility in the United States, Britain, and Japan (comparing mobility in these countries) and (2) data on the association between religion and voting behavior in U.S. presidential elections from 1968 to 1992 (comparing this association in the different elections). We also introduce here graphical displays that can be used to obtain worthwhile information about goodness-of-fit and to aid in substantive interpretation.     

Explaining the Flight of Cupid’s Arrow: A Spatial Random Utility Model of Partner Choice

Spatial homogamy may be defined as follows: anyone may be attracted to anyone else, but near candidates are more attractive than distant candidates. In this article, we propose a model of partner choice, where homogamy is defined in terms of spatial, demographic, socioeconomic and cultural similarity. A spatial choice model using random utility theory is formulated, taking into account a relaxation of the independence from the irrelevant alternatives property, as spatial alternatives are not independent of one another. We model partner choice given the characteristics of the chosen partner and a choice set of alternatives, using unique micro data on all new cohabiters in the Netherlands, linked to other relevant data sets. The model takes the spatial locations of potential candidates within a choice set into account, including an indicator for the spatial similarity between alternatives. We find that spatial homogamy is a vital component of partner matching, aside from and adding to the spatial effects in demographic, socioeconomic and cultural homogamy. Given a choice set of partners, the highest likelihood of a match occurs with a person who is born and lives near by, who is close in age, is in the same life stage and has the same marital status, who has the same educational and income level and the same labour market status, who speaks the same dialect and lives in a culturally similar residential area. The distance effect is most pronounced for those individuals with lower levels of education and those living in rural areas.     

Multilevel maximum likelihood estimation with application to covariance matrices

The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of covariance models to the sample, which is important in data assimilation. The hierarchical maximum likelihood approach is applied to the spectral diagonal covariance model with different parameterizations of eigenvalue decay, and to the sparse inverse covariance model with specified parameter values on different sets of nonzero entries. It is shown computationally that using smaller sets of parameters can decrease the sampling noise in high dimension substantially.     

Mathematical programming: Turing completeness and applications to software analysis

Mathematical programming is Turing complete, and can be used as a general-purpose declarative language. We present a new constructive proof of this fact, and showcase its usefulness by discussing an application to finding the hardest input of any given program running on a Minsky Register Machine. We also discuss an application of mathematical programming to software verification obtained by relaxing one of the properties of Turing complete languages.