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Hierarchical Log-linear Models for Contingency Tables

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Brzezińska J.
Acta Universitatis Lodziensis. Folia Oeconomica
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2012
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vol. 269
EN
Log-linear models are widely used for qualitative data in multidimensional contingency tables. Hierarchical log-linear models are models that include all lower-order terms composed from variables contained in a higher-order model term. The starting point is a saturated model, then homogenous associations, conditional independence and complete independence. There are several statistics that help to choose the best model. The first is the likelihood ratio approach, next is AIC and BIC information criteria. In R software there is loglm() function in MASS library and glm in stats library. The first approach is presented in this paper
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Analysis of Censored Life-tables with Covariates by Means of Log-linear Models

100%
Rossa A., University of Łódź D. o. S. M.
Acta Universitatis Lodziensis. Folia Oeconomica
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2004
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vol. 175
EN
In survival analysis the subject of observation is duration of time until some event called failure event. Often in such studies only partial information on the length of failure time is available what yields the so-called right-censored observations. The main interest in survival analysis is either to estimate the distribution of the true failure time or to identify the relationship between the true failure time and a set of some covariates. Additional troublesome point of theory and application of survival techniques is treatment of grouped observations (life-tables) along with incorporating covariates. In the paper a new approach is considered which allows to treat the censored life-table with qualitative covariates as a standard contingency table. Such a table can be further analysed by means of log-linear models or other standard multivariate inference techniques.
PL
W pracy przedstawiono propozycję analizy tablicy trwania życia dla danych prawostronnie cenzurowanych. Przedstawiona metoda pozwala na sprowadzenie takiej tablicy do wielowymiarowej tablicy kontyngencyjnej, którą można analizować standardowymi technikami wielowymiarowego wnioskowania statystycznego, np. za pomocą modeli logarytmiczno-liniowych.
3
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Latent class analysis in the evaluation of items in survey research

100%
Brzezińska J.
Econometrics. Ekonometria. Advances in Applied Data Analytics
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2018
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issue vol. 22 no. 3
55-65
EN
Latent class analysis has been widely used in the measurement models. Models based on latent variables have a wide range of applications in the presence of repeated ob-servations, longitudinal data, and multilevel data. In this paper we present and apply log-linear analysis as a method for the analysis of multi-way tables. We also present a latent variable model based on a variable that is not directly observed. The basic model postulates an underlying categorical latent variable; within any category of the latent variable the manifest or observed categorical variables are assumed independent of one another (axiom of conditional independence). In this paper we present the results of a survey research based on categorical data and the author`s questionnaire. We present the results of the latent class analysis in the classification of respondents into clusters characterized by similar attitudes and features in economic research. We also conduct a prior log-linear analysis for a multi-way contingency table. All the calculations are conducted in R.
4
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Influence of the source of information on homophily assessment: data provided by subjects vs data provided by their confidants

88%
Kęska A., Przybysz D., Mach B. W.
ASK. Research and Methods
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2021
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vol. 30
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issue 1
3-24
EN
The present article analyses data on ego-centred networks from a nationally representative sample of Polish citizens (egos) and their regular conversation partners (alters). In the study being used, apart from obtaining information from the respondent (the ego) about characteristics of their friends (alters), the respondent was additionally asked to provide contact details for his/her alters and the interviewers traced them. This allows to compare data concerning alters obtained from ego and from alters themselves. In the first part of the article, a comparison for three characteristics – age, education and occupational status – is provided as well as patterned differences are presented. In the second part, the issue whether the assessment of the strength of homophily depends on the source information about the alters is raised. The differences are present, although they are rather slight. The authors observe greater homophily when they rely on the responses of the ego. Based on the results, recommendations for future research on ego-centred networks are formulated.
5
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Graphical Presentation of a Multi - Way Contingency Table in the R Software

88%
Kasprzyk I., Department of Statistics T. K. A. U. o. E.
Acta Universitatis Lodziensis. Folia Oeconomica
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2009
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vol. 228
PL
Tablica kontyngencji jest częstym sposobem przedstawiania danych mierzonych zarówno na skali nominalnej jak i porządkowej. W referacie zostaną przedstawione różne typy modeli log-liniowych, które pozwalają na badanie zależności między zmiennymi zawartymi w tablicy kontyngencji. Za pomocą pakietu vcd oraz graphics w programie R zostanie dokonana wizualizacja danych zawartych w wielowymiarowej tablicy kontyngencji Zostaną przedstawione przede wszystkim wykresy mozaikowe, które to są najczęstszym sposobem wizualizacji modeli log-liniowych. Tego typu wykresy mozaikowe zostały zaproponowane przez Hartigan i Kleiner [1981]. Referat jest kontynuacją referatu „Wizualizacja dwuwymiarowych tablic kontyngencji w pakiecie statystycznym R” wygłoszonego na XXV Konferencji MSA 2006.
EN
The contingency table is a popular way of presenting categorical data. This paper presents the various types of the log-linear models, which describe the relationship between variables in the contingency table. We can make a visualisation of data contained in the multi-way contingency table using the vcd and graphics packages in the R software. The main aim of this paper is to show the mosaic plots, which are the most popular ways of visualization of this kind of models. The mosaic display was proposed by Hartigan and Kleiner (1981). This paper is a continuation of the paper titled “Visualizing of a two-way contingency table in the R software” delivered at the conference on Multivariate Statistical Analysis in 2006.
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