The aim of this work is to evaluate the intensity of possible secular trends among the five subsequent cohorts of Wrocław (Poland) children aged 0, 6, 12 and 24 months. This document describes secular changes in the body length, weight and the Rohrer’s index. Material: Research material represent the longitudinal studies of five consecutive birth cohorts. The first study involved children born during 1963-1965, and the last in 2003-2005. All of the studies were related to the same social group and were conducted using the same methodology. There are differences in the intensity and direction of the secular trends in children depending on their age. In both sexes the body length of newborns kept increasing until the end of the nineties and decreased in the last decade. The body weight did not change during the 40-year period. This suggests an important role of maternal regulator in fetal development and therefore no clear response to external environmental factors. Secular changes such as the body length and weight, which are the most adequate to the economic changes in Poland, were observed in children aged 6 and 12 months. It may be a result of their highest ecosensitivity during this period. However, there have not been any clear trends observed in the 24 months age group. This may be due to the increasing participation of genetic factors in the development of the child.
The problem of modeling longitudinal profiles is considered assuming that the population and elements affiliation to subpopulation may change in time. The considerations are based on a model with auxiliary variables for longitudinal data with subject specific (in this case - element and subpopulation specific) random components (compare Verbeke, Molenberghs, 2000; Hedeker, Gibbons, 2006) which is a special case of the General Linear Mixed Model. In the paper calibration estimators of subpopulation total for data from one period are presented and some modifications for the case of longitudinal data are proposed. Design-based mean squared errors and its estimators are also presented. In the simulation study accuracy of the estimators is compared with Horvitz-Thomson estimator and the best empirical linear unbiased predictor derived for the considered model.
This article describes a unique version of a longitudinal database featuring the Eastern Europe Parliamentarian and Candidate Database (EAST PaC). This version contains contextual and biographical information on career politicians from Poland, 1985-2007. I define career politicians as those who, three times during the period covered in the data, were granted a parliamentary seat in either the upper (Senat) or lower house (Sejm). As part of this project, I reconstructed the political biographies of career politicians. Based on practical experience in using these data, I propose the use of relational databases as a best practices approach to manage data of this type. I describe the need for relational databases in general, and describe in detail how to apply them to longitudinal data consisting of parliamentarians and their contexts.
Good graphical presentation of data is useful during the whole analysis process from the first glimpse into the data to the model fitting and presentation of results. The most popular way of longitudinal data presentation are separate (for each wave, in cross-sectional dimension) comparisons of figures. However, plotting the data over time is useful in suggesting appropriate modeling techniques to deal with the heterogeneity observed in the trajectories. The main aim of this paper is to present the changing perceptions of the financial situation in Poland using different graphical tools for the heterogonous discrete longitudinal data sets and present demographics features for those changes. We will focus on the most important features of the categorical longitudinal data – category sequences and their graphical presentation. We aim to characterize the analyzed sequences on the basis of unidimensional indicators and composite complexity measures, as well as using mainly TraMineR [Gabadinho et al. 2017] package of R.
The functional principal components analysis joins the advantages of the principal components analysis and provide analysis of dynamic data. The main difference in both methods is the type of data the PCA is based on multivariate data, whereas the FPCA on the functional data including curves and trajectories, i.e. a series of individual observations, not a single observation, as usual. The functional principal components analysis with functional data, will be used in the analysis. This method allows the analysis of dynamic data. The purpose of the article is to apply of functional principal components analysis to the problem of student’s achievements. The article was compared the level of students' knowledge during different stages of education in 2009-2017. The analysis covers the average exam results after the II, III and IV stage of education.
The problem of modeling longitudinal profiles is considered assuming that the population and elements affiliation to subpopulations may change in time. The considerations are based on a model with auxiliary variables for longitudinal data with element and subpopulation specific random components (compare Verbeke, Molenberghs, 2000; Hedeker, Gibbons, 2006) which is a special case of the General Linear Model (GLM) the General Linear Mixed Model (GLMM). In the paper the pseudo-empirical best linear unbiased predictor (Pseudo-EBLUP) based on model-assisted approach will be presented along with its mean squared error (MSE) and its estimators. In the simulation study its accuracy will be compared with some calibration estimators which are based on model-assisted approach too.
The problem of modeling longitudinal profiles is considered assuming that the population and elements’ affiliation to subpopulations may change in time. Some longitudinal model which is a special case of the general linear model (GLM) and the general linear mixed model (GLMM) is studied. In the model two random components are included under assumptions of simultaneous spatial autoregressive process (SAR) and temporal first-order autoregressive process (AR(1)) respectively. The accuracy of model parameters’ restricted maximum likelihood estimators is considered in the simulation.
PL
Rozważany jest problem modelowania profili wielookresowych zakładając, że populacja i przynależność elementów domen mogą zmieniać się w czasie. Proponowany model jest przypadkiem szczególnym ogólnego modelu liniowego i ogólnego mieszanego modelu liniowego. W modelu tym uwzględniono dwa wektory składników losowych spełniające odpowiednio założenia przestrzennego modelu autoregresyjnego i modelu autoregresyjnego rzędu pierwszego w czasie. W symulacji rozważano dokładność estymatorów parametrów modelu uzyskanych metodą największej wiarygodności z ograniczeniami.
The objective of the research was to prepare longitudinal percentile curves for the BMI (kg/m2) relative to time before and after peak height velocity (PHV) in Japanese boys and girls born between 1989 and 1991. Stature and weight were measured in every April from 6.5 to 16.5 years for 283 boys and 480 girls. Age at PHV was estimated by the proportional allotment method. The 50th percentile curves for the BMI of Japanese boys and girls born between 1989 and 1991 were similar to the corresponding curves for Japanese boys and girls born between 1972 and 1974. However, the 97th percentiles of children born between 1989 and 1991 were higher and the corresponding 3rd percentiles were lower compared to children born between 1972 and 1974. The differences can be attributed to the influence of early maturing children born between 1989 and 1991 on the 97th percentiles and of late maturing children born between 1989 and 1991 on the 3rd percentiles. The results highlight the need to consider the timing of maturity, in this case, age at PHV, when interpreting the BMI of adolescents.
Analiza głównych składowych (PCA) polega na transformacji zmiennych pierwotnych w zbiór nowych wzajemnie ortogonalnych zmiennych, zwanych głównymi składowymi. Funkcjonalna analiza głównych (FPCA) składowych ma zalety klasycznej analizy głównych składowych, dodatkowo umożliwia analizę danych o charakterze dynamicznym. Podstawową różnicą między tymi dwiema metodami jest rodzaj danych: PCA bazuje na danych wielowymiarowych, natomiast FPCA na danych funkcjonalnych. Danymi funkcjonalnymi są krzywe i trajektorie, czyli ciąg indywidualnych obserwacji, a nie pojedyncza obserwacja. Celem artykułu jest pokazanie możliwości wykorzystania funkcjonalnej analizy głównych składowych do badania zjawisk opisanych danymi wzdłużnymi (longitudinal data). Przykład wykorzystania tej metody omówiony w artykule opiera się na analizie zmiany liczby studentów w czasie w wybranych krajach europejskich. Możliwości wizualizacyjne metody pozwalają na porównanie krajów i wyodrębnienie obserwacji odstających.
EN
Principal component analysis (PCA) transforms an original set of variables into a new orthogonal set called principal components. Functional principal component analysis (FPCA) has the same advantages as classical principal component analysis while also enabling the analysis of dynamic data. The main difference between them is that PCA is based on multidimensional data and FPCA is based on functional data. The functional data are curves, surfaces or anything else varying over a continuum. They are not a single observation. The main aim of the paper is to show the usefulness of applying functional principal component analysis in order to analyse longitudinal data. The paper presents an example of how this method has been used based on the analysis of changes in the number of students (over time) in chosen European countries. Visualisation of the results makes it possible to compare countries and detect outliers.
Cel: Celem badania jest określenie wpływu zmiennych socjodemograficznych (tj. wiek, wykształcenie, stan cywilny, status społeczno-zawodowy) na nastawienie do emigracji po wejściu Polski do UE. Metodyka: Zastosowano ukryty model Markowa z wykorzystaniem zmiennych towarzyszących, mających wpływ nie na ukrytą, lecz na obserwowaną część modelu LM. Model ten, uwzględniający zmienne w czasie efekty losowe, został wykorzystany w celu analizy zbioru panelowego dotyczącego gotowości Polaków do pracy zagranicą w latach 2005–2015. Wyniki: Opierając się na polskim panelowym badaniu społecznym, tj. Diagnozie Społecznej, pokazano, że analizowany zbiór można wyjaśnić za pomocą dwóch stanów ukrytych, charakteryzujących się podobną skłonnością do emigracji. Zaobserwowano, że w latach 2011–2015 (następujących po pierwszej fazie akcesyjnej) Polacy wykazali większą stabilność w poglądach dotyczących emigracji. Na podstawie dostępnych (stałych i zmiennych w czasie) zmiennych towarzyszących pokazano, że osoby o pewnych cechach są bardziej skłonne do migracji niż inne. Implikacje i rekomendacje: Przedstawione podejście może być zastosowane w celu ukazania zmieniających się zachowań społecznych również w innych krajach, które doświadczyły masowego odpływu ludności. Ponadto analiza uzyskanych wyników może posłużyć rozwiązywaniu wyzwań politycznych i skutecznemu zarządzaniu migracją, także w przypadku przyszłych danych, dotyczących nastawienia do ukraińskich uchodźców przybywających obecnie do Polski. Oryginalność/wartość: Główną zaletą zastosowanego modelu, w porównaniu z standardowym modelem z efektami losowymi lub modelem klas ukrytych ze zmiennymi towarzyszącymi, jest to, że nieobserwowalna heterogeniczność może być zmienna w badanym czasie. Inaczej niż w badaniach poprzednich założono tu, że udzielane odpowiedzi respondentów mogą różnić się z powodu nieobserwowalnej, zmiennej w czasie współzmiennej, takiej jak „uczucia patriotyczne”. Zastosowany model, uwzględniający również wagi badania panelowego, pozwala także na uzyskanie lepszego dopasowania w porównaniu ze standardowym modelem efektów losowych, zaś parametry modelu LM umożliwiają dodatkowo ocenę dynamiki badanej zmiennej ukrytej.
EN
Aim: Since 2004 European countries, such as Germany and the United Kingdom, have noted an unusual upward trend of migrants from Central and Eastern Europe. The author aimed to examine the popular perception of emigration from Poland in the years following EU accession. Moreover, the study presents the effect of the observed socio-economic features (i.e. age, education, marital status, socio-professional status) affecting the conditional probabilities of the response variable, considering also the unobserved heterogeneity between the respondents representing Polish society. Methodology: The study was based on the Latent Markov (LM) models which allowed finding homogenous groups of respondents on the basis of their definite responses measured at different points in time. The author compared the respondents behaviour in the groups arriving just after EU accession, in relation to the other surveyed surges in migration using the Latent Markov models with different types of constraints. Then, to show the effect of observable socio-economic characteristics, taking into account the unobserved heterogeneity between the subjects, the study employed the version including the covariates in the measurement part of the model. Results: Based on the Polish longitudinal social survey, i.e. Social Diagnosis, the study shows that the analysed data can be explained by two latent states of Poles sharing the same propensity towards emigration. It was observed that Poles were more stable in their feelings concerning their approach to the emigration in the period 2011–2015 (following the first post-accession phase). Based on the available (time-constant and time-varying) covariates, the author demonstrated that certain types of people are more prone to migrate than others. Implications and recommendations: The presented approach could be applied to data from other economies – both within the EU and outside it – which have also seen massive outflows of people, to show the changing behaviour of society. This methodology might also be helpful with policy challenges and the effective management of migration, as well as for future data concerning the attitudes towards refugees from Ukraine coming to Poland at present. Originality/value: Unlike previous studies, the author assumed that the attitudes toward emigration can vary on the response variable, i.e. because of the unobserved covariate such as ‘patriotic behaviour’ (unobserved heterogeneity), which may change over time. The study applied the appropriate LM techniques extended to include the covariates in the measurement part of the LM model and the longitudinal weights of the survey. Note that the applied model also allowed achieving a better measure-of-fit compared to the standard random-effect model, and the parameters of the LM model additionally enabled to evaluate the dynamic of the latent trait.
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