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The Italian market of sparkling wines increases as volume and assortment (such as brands, appellations, typologies) mainly because of sparkling Prosecco consumption. We investigate the repeated purchase behavior of sparkling wines in two years within the supermarket channel through scanner data collected from a consumer panel. We propose a Hidden Markov Model to analyze these data, assuming an unobservable process to capture consumers’ preferences and allowing us to consider purchases sparsity over time. We consider multivariate responses defining types of purchases, namely price, appellation, and sugar content. Customers’ covariates influence the initial and transition probabilities of the latent process. We identify five market segments, and we track their evolution over time. One segment includes Prosecco-oriented consumers, and we show that loyalty to Prosecco changes strongly over time according to the region of residence, income, and family type. The findings improve the understanding of the market and may provide evidence to design successful marketing strategies. (JEL Classifications: C33, C51, D12, L66)

We investigate public trust among the society by a statistical model suitable for panel data. At this aim, using trust’s levels measured from individual items recorded through a long-term survey we dispose of key variables with appropriate meaning. We account for the repeated and missing item responses by a hidden Markov model using longitudinal sampling weights. Since trust may be conceived as a psychological unobservable process of each person that fluctuates over time we consider observed time-varying and time-fixed individual covariates. We estimate the model parameters by a weighted log-likelihood through the Expectation–Maximization algorithm by using data collected in an East-Central European country like Poland. The latter is a country where the level of support to the national and international institutions is one of the lowest among the European member states. We apply a suitable algorithm based on the posterior probabilities to predict the best allocation to each latent typology. The proposed model is validated by generating out-of-sample responses and we find reasonable predictive values. We disentangle four hidden groups of Poles: discouraged, with no opinion, with selective trust and with fully public trust. We reveal an increasing number of people that are going to trust only some selected institutions over time.

We aim to monitor financial asset price series by a generalized version of the moving average convergence/divergence (MACD) trend indicator which is currently employed as technical indicator in trading systems. We use the proposed indicator to test the semi-strong form of market efficiency hypothesis stating that asset prices follows a martingale model when, on the basis of the information available up to a given time, the expected returns are equal to zero. By assuming a martingale model with drift for prices, we propose an MACD-based test statistic for the local drift and derive its main theoretical properties. The semi-strong market efficiency hypothesis is assessed through a nonparametric bootstrap test, where under the null hypothesis the prices have no drift. A simulation study shows that the empirical size and power of the bootstrap test rapidly converges to the chosen nominal levels. Finally, we use our test to derive a long/short equity trading strategy where no active positions are taken or maintained under the null hypothesis (no drift). We apply this strategy to monitor 1,469 daily quotes of the crude oil prices over the six year period 2010-2016 finding that our methodology is often capable to detect market inefficiencies by accruing positive returns.

Latent Markov (LM) models represent an important class of models for the analysis of longitudinal data, especially when response variables are categorical. These models have a great potential of application in many fields, such as economics and medicine. We illustrate the R package LMest that is tailored to deal with the basic LM model and some extended formulations accounting for individual covariates and for the presence of unobserved clusters of units having the same initial and transition probabilities (mixed LM model). The main functions of the package are tailored to parameter estimation through the expectation-maximization algorithm, which is based on suitable forwardbackward recursions. The package also permits local and global decoding and to obtain standard errors for the parameter estimates. We illustrate the use of the package and its main features through some empirical examples in the fields of labour market, health, and criminology.

We exploit a multivariate multilevel model for the analysis of the Italian sample of the TIMSS\&PIRLS 2011 Combined International Database on fourth grade students. The multivariate approach jointly considers educational achievement on Reading, Mathematics and Science, thus allowing us to test for differential associations of the covariates with the three outcomes, and to estimate the residual correlations between pairs of outcomes at student and class levels. Multilevel modelling allows us to disentangle student and contextual factors affecting achievement. We also account for territorial differences in wealth by means of an index from an external source. The model residuals point out classes with high or low performance. As educational achievement is measured by plausible values, the estimates are obtained through multiple imputation formulas. The results, while confirming the role of traditional student and contextual factors, reveal interesting patterns of achievement in Italian primary schools., 25 pages, 5 figures, Presented at the VI European Congress of Methodology, 23-25 July 2014, Utrecht, Netherlands; Presented at the 47th Scientific meeting of the Italian Statistical Society, 11-13 June 2014, Cagliari, Italy

Summary Motivated by an application to a longitudinal data set coming from the Health and Retirement Study about self-reported health status, we propose a model for longitudinal data which is based on a latent process to account for the unobserved heterogeneity between sample units in a dynamic fashion. The latent process is modelled by a mixture of auto-regressive AR(1) processes with different means and correlation coefficients, but with equal variances. We show how to perform maximum likelihood estimation of the proposed model by the joint use of an expectation–maximization algorithm and a Newton–Raphson algorithm, implemented by means of recursions developed in the hidden Markov model literature. We also introduce a simple method to obtain standard errors for the parameter estimates and suggest a strategy to choose the number of mixture components. In the application the response variable is ordinal; however, the approach may also be applied in other settings. Moreover, the application to the self-reported health status data set allows us to show that the model proposed is more flexible than other models for longitudinal data based on a continuous latent process. The model also achieves a goodness of fit that is similar to that of models based on a discrete latent process following a Markov chain, while retaining a reduced number of parameters. The effect of different formulations of the latent structure of the model is evaluated in terms of estimates of the regression parameters for the covariates.

We propose an extension of the latent class model for the analysis of capture-recapture data which allows us to take into account the effect of a capture on the behavior of a subject with respect to future captures. The approach is based on the assumption that the variable indexing the latent class of a subject follows a Markov chain with transition probabilities depending on the previous capture history. Several constraints are allowed on these transition probabilities and on the parameters of the conditional distribution of the capture configuration given the latent process. We also allow for the presence of discrete explanatory variables, which may affect the parameters of the latent process. To estimate the resulting models, we rely on the conditional maximum likelihood approach and for this aim we outline an EM algorithm. We also give some simple rules for point and interval estimation of the population size. The approach is illustrated by applying it to two data sets concerning small mammal populations. © 2006, The International Biometric Society.

We extend to the longitudinal setting a latent class approach that was recently introduced by Lanza, Coffman, and Xu to estimate the causal effect of a treatment. The proposed approach enables an evaluation of multiple treatment effects on subpopulations of individuals from a dynamic perspective, as it relies on a latent Markov (LM) model that is estimated taking into account propensity score weights based on individual pretreatment covariates. These weights are involved in the expression of the likelihood function of the LM model and allow us to balance the groups receiving different treatments. This likelihood function is maximized through a modified version of the traditional expectation–maximization algorithm, while standard errors for the parameter estimates are obtained by a nonparametric bootstrap method. We study in detail the asymptotic properties of the causal effect estimator based on the maximization of this likelihood function, and we illustrate its finite sample properties through a series of simulations showing that the estimator has the expected behavior. As an illustration, we consider an application aimed at assessing the relative effectiveness of certain degree programs on the basis of three ordinal response variables in which the work path of a graduate is considered as the manifestation of his or her human capital-level across time.

We introduce a model for categorical panel data which is tailored to the dynamic evaluation of the impact of job training programs. The model may be seen as an extension of the dynamic logit model in which unobserved heterogeneity between subjects is taken into account by the introduction of a discrete latent variable. For the estimation of the model parameters we use an EM algorithm and we compute standard errors on the basis of the numerical derivative of the score vector of the complete data log-likelihood. The approach is illustrated through the analysis of a dataset containing the work histories of the employees of the private firms of the province of Milan between 2003 and 2005, some of whom attended job training programs supported by the European Social Fund.