Regression analysis of compositional data when both the dependent variable and independent variable are components

It is well known that regression analyses involving compositional data need special attention because the data are not of full rank. For a regression analysis where both the dependent and independent variable are components we propose a transformation of the components emphasizing their role as dependent and independent variables. A simple linear regression can be performed on the transformed components. The regression line can be depicted in a ternary diagram facilitating the interpretation of the analysis in terms of components. An exemple with time-budgets illustrates the method and the graphical features

When zero doesn't mean it and other geomathematical mischief

There is almost not a case in exploration geology, where the studied data doesn’t includes below detection limits and/or zero values, and since most of the geological data responds to lognormal distributions, these “zero data” represent a mathematical challenge for the interpretation. We need to start by recognizing that there are zero values in geology. For example the amount of quartz in a foyaite (nepheline syenite) is zero, since quartz cannot co-exists with nepheline. Another common essential zero is a North azimuth, however we can always change that zero for the value of 360°. These are known as “Essential zeros”, but what can we do with “Rounded zeros” that are the result of below the detection limit of the equipment? Amalgamation, e.g. adding Na2O and K2O, as total alkalis is a solution, but sometimes we need to differentiate between a sodic and a potassic alteration. Pre-classification into groups requires a good knowledge of the distribution of the data and the geochemical characteristics of the groups which is not always available. Considering the zero values equal to the limit of detection of the used equipment will generate spurious distributions, especially in ternary diagrams. Same situation will occur if we replace the zero values by a small amount using non-parametric or parametric techniques (imputation). The method that we are proposing takes into consideration the well known relationships between some elements. For example, in copper porphyry deposits, there is always a good direct correlation between the copper values and the molybdenum ones, but while copper will always be above the limit of detection, many of the molybdenum values will be “rounded zeros”. So, we will take the lower quartile of the real molybdenum values and establish a regression equation with copper, and then we will estimate the “rounded” zero values of molybdenum by their corresponding copper values. The method could be applied to any type of data, provided we establish first their correlation dependency. One of the main advantages of this method is that we do not obtain a fixed value for the “rounded zeros”, but one that depends on the value of the other variable. Key words: compositional data analysis, treatment of zeros, essential zeros, rounded zeros, correlation dependency

An alternative method for dating unknown tephras based on a segmented regression model

In CoDaWork’05, we presented an application of discriminant function analysis (DFA) to 4 different compositional datasets and modelled the first canonical variable using a segmented regression model solely based on an observation about the scatter plots. In this paper, multiple linear regressions are applied to different datasets to confirm the validity of our proposed model. In addition to dating the unknown tephras by calibration as discussed previously, another method of mapping the unknown tephras into samples of the reference set or missing samples in between consecutive reference samples is proposed. The application of these methodologies is demonstrated with both simulated and real datasets. This new proposed methodology provides an alternative, more acceptable approach for geologists as their focus is on mapping the unknown tephra with relevant eruptive events rather than estimating the age of unknown tephra. Kew words: Tephrochronology; Segmented regression

Regression periods in infancy. A case study from Catalonia.

Based on Rijt-Plooij and Plooij’s (1992) research on emergence of regression periods in the first two years of life, the presence of such periods in a group of 18 babies (10 boys and 8 girls, aged between 3 weeks and 14 months) from a Catalonian population was analyzed. The measurements were a questionnaire filled in by the infants’ mothers, a semi-structured weekly tape-recorded interview, and observations in their homes. The procedure and the instruments used in the project follow those proposed by Rijt-Plooij and Plooij. Our results confirm the existence of the regression periods in the first year of children’s life. Inter-coder agreement for trained coders was 78.2% and within-coder agreement was 90.1 %. In the discussion, the possible meaning and relevance of regression periods in order to understand development from a psychobiological and social framework is commented upon

Simultaneous estimation of indirect and interaction effects using structural equation models

Interaction effects are usually modeled by means of moderated regression analysis. Structural equation models with non-linear constraints make it possible to estimate interaction effects while correcting for measurement error. From the various specifications, Jöreskog and Yang's (1996, 1998), likely the most parsimonious, has been chosen and further simplified. Up to now, only direct effects have been specified, thus wasting much of the capability of the structural equation approach. This paper presents and discusses an extension of Jöreskog and Yang's specification that can handle direct, indirect and interaction effects simultaneously. The model is illustrated by a study of the effects of an interactive style of use of budgets on both company innovation and performance

Use of multilevel logistic regression to identify the causes of differential item functioning

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Regression-based techniques for statistical decision making in singlecase designs

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La qualitat educativa a l'ESO : an??lisi multivariable d'una selecci?? d'indicadors educatius. 'La calidad educativa en la ESO : an??lisis multivariable de una selecci??n de indicadores educativos'

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Additional regression techniques_Solutions_2009.ppt (19)

PowerPoint Slides relating to theory and use of SPSS. Used in Research Skills for Biomedical Science

Curva de aprendizaje para ventana ecográfica de la vena cava inferior, en residentes de medicina de emergencias

INTRODUCCIÓN. El ultrasonido es fundamental en la medicina de emergencias, no se conoce cual debería ser la curva de aprendizaje para obtener las competencias técnicas y operativas; ACEP recomienda por cada ventana ecográfica realizar 25 repeticiones. No existe una curva de aprendizaje para ventana de VCI en la población de residentes colombianos. OBJETIVO: Determinar la curva de aprendizaje necesaria para obtener una proporción mayor al 80% de éxitos en la toma de la ventana ecográfica de la VCI, usando la escala de calificación para el aseguramiento de la calidad sugerida por ACEP, en residentes de I a III año de medicina de emergencias. METODOLOGÍA: Estudio experimental no comparativo, que evaluó la proporción de éxito en función del las tomas repetidas de la VCI por ultrasonido, mediciones que se tomaron luego de participar en una capacitación teórica y demostrativa de la técnica propuesta; se calificaron los videos según la escala publicada por ACEP. El análisis estadístico se realizó con un modelo logístico multinivel para la proporción del éxito, agrupado por repetición y agrupado por sujeto. RESULTADOS: Se obtuvo información de 8 residentes, cada uno realizo 25 repeticiones a 3 modelos sanos con asignación aleatoria. Se realizó la curva de aprendizaje obteniendo en 11 repeticiones una proporción de 0.80 (rango 0.54 a 0.92) y en 21 repeticiones una proporción de 0.9 (rango 0.75 a 0.96), datos ajustados por numero de repetición y residente. CONCLUSIÓN: La curva de aprendizaje para la ventana ecográfica de la VCI es de 11 y 21 repeticiones para obtener el 80% y 90% de éxito en residentes de medicina de emergencias de I a III año de la universidad del rosario.

Sample size requirements for interval estimation of the strengthof association effect sizes in multiple regression analysis

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A comparison of discriminant logistic regression and Item Response Theory Likelihood-Ratio Tests for Differential Item Functioning (IRTLRDIF) in polytomous short tests

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