Correcting Measurement Error Bias in Interaction Models with Small Samples

Several methods have been suggested to estimate non-linear models with interaction terms in the presence of measurement error. Structural equation models eliminate measurement error bias, but require large samples. Ordinary least squares regression on summated scales, regression on factor scores and partial least squares are appropriate for small samples but do not correct measurement error bias. Two stage least squares regression does correct measurement error bias but the results strongly depend on the instrumental variable choice. This article discusses the old disattenuated regression method as an alternative for correcting measurement error in small samples. The method is extended to the case of interaction terms and is illustrated on a model that examines the interaction effect of innovation and style of use of budgets on business performance. Alternative reliability estimates that can be used to disattenuate the estimates are discussed. A comparison is made with the alternative methods. Methods that do not correct for measurement error bias perform very similarly and considerably worse than disattenuated regression

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

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

Time-series regression models to study the short-term effects of environmental factors on health

Time series regression models are especially suitable in epidemiology for evaluating short-term effects of time-varying exposures on health. The problem is that potential for confounding in time series regression is very high. Thus, it is important that trend and seasonality are properly accounted for. Our paper reviews the statistical models commonly used in time-series regression methods, specially allowing for serial correlation, make them potentially useful for selected epidemiological purposes. In particular, we discuss the use of time-series regression for counts using a wide range Generalised Linear Models as well as Generalised Additive Models. In addition, recently critical points in using statistical software for GAM were stressed, and reanalyses of time series data on air pollution and health were performed in order to update already published. Applications are offered through an example on the relationship between asthma emergency admissions and photochemical air pollutants

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

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

Networks of PhD Students and Academic Performance: A Comparison across Countries

In this article we compare regression models obtained to predict PhD students’ academic performance in the universities of Girona (Spain) and Slovenia. Explanatory variables are characteristics of PhD student’s research group understood as an egocentered social network, background and attitudinal characteristics of the PhD students and some characteristics of the supervisors. Academic performance was measured by the weighted number of publications. Two web questionnaires were designed, one for PhD students and one for their supervisors and other research group members. Most of the variables were easily comparable across universities due to the careful translation procedure and pre-tests. When direct comparison was not possible we created comparable indicators. We used a regression model in which the country was introduced as a dummy coded variable including all possible interaction effects. The optimal transformations of the main and interaction variables are discussed. Some differences between Slovenian and Girona universities emerge. Some variables like supervisor’s performance and motivation for autonomy prior to starting the PhD have the same positive effect on the PhD student’s performance in both countries. On the other hand, variables like too close supervision by the supervisor and having children have a negative influence in both countries. However, we find differences between countries when we observe the motivation for research prior to starting the PhD which increases performance in Slovenia but not in Girona. As regards network variables, frequency of supervisor advice increases performance in Slovenia and decreases it in Girona. The negative effect in Girona could be explained by the fact that additional contacts of the PhD student with his/her supervisor might indicate a higher workload in addition to or instead of a better advice about the dissertation. The number of external student’s advice relationships and social support mean contact intensity are not significant in Girona, but they have a negative effect in Slovenia. We might explain the negative effect of external advice relationships in Slovenia by saying that a lot of external advice may actually result from a lack of the more relevant internal advice

El Conjunt instrumental Orff com a dinamitzador de la motivació en els alumnes de música d’educació secundària

L’estudi que es presenta a continuació aporta una experiència a l’entorn de l’efectivitat del CIO com a material capaç d’incentivar un canvi en l’actitud i en la implicació de l’alumnat d’ESO cap a l’assignatura de música. Aquesta investigació va néixer com a conseqüència de la necessitat d’estimular la motivació personal dels alumnes de dos grups-classe d’ESO cap a la matèria després de detectar la manca d’interès i la facilitat amb què es distreien a l’aula. Aquesta percepció es va poder corroborar mitjançant la realització d’uns qüestionaris informals realitzats a finals del curs 2005-2006 on es demanava a l’alumnat que escrivissin tres aspectes positius i tres de negatius del que havien fet a l’assignatura durant aquell curs. Amb aquesta breu indagació es va confirmar que l’opinió més generalitzada entre l’alumnat era que s’avorrien sovint a les classes perquè eren massa teòriques. Arran d’aquests resultats, es va decidir canviar l’orientació de l’assignatura per tal d’estimular el “fer música” per davant de la “transmissió” de continguts més conceptuals. De les diverses opcions possibles, es va optar per introduir el CIO com a eina per fer possible aquest canvi, ja que algunes experiències educatives prèvies realitzades amb aquest tipus de material demostraven que la intervenció amb els instruments Orff podia contribuir a incrementar l’interès de l’alumnat cap a la matèria i alhora aportar nombrosos beneficis per a la pràctica musical