A heteroscedastic structural errors-in-variables model with equation error

Patriota, Alexandre G.; Bolfarine, Heleno; Castro, Mário de

doi:10.1016/j.stamet.2009.02.003

Cited by 32 publications

(28 citation statements)

References 8 publications

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“…., , n. n. For each segment For each segment rates are then computed as rates are then computed as ature (e.g., Cheng & Riu, 2006;Kulathinal, Kuulasmaa, & 283 Gasbarra, 2002;Patriota, Bolfarine, 284 & de Castro, 2009). When the measurement-error variance is 285 small, as in the application here, the method of moments 286 (Patriota et al, 2009) provides an efficient estimate of the 287 slope that is simple to compute. This approach will be used 288…”

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confidence: 99%

Methodological Advances for Detecting Physiological Synchrony During Dyadic Interactions

et al. 2013

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The synchronization of oscillatory systems -or coupled 24 oscillations -is widely studied in the biological and physical 25 sciences (e.g., Mirollo & Strogatz, 1990; Pikovsky, 26 Rosenblum, & Kurths, 2001; Weishenbush, Nishioka, Ishik-27 awa, & Arakawa, 1992), with also multiple applications in 28 the social sciences, economics, and medicine (e.g., Quian 29 Quiroga, Kraskov, Kreuz, & Grassberger, 2002). The syn-30 chrony of these oscillations can provide information about 31 the system not available from separate univariate analyses. 32Consider, for example, the investigation of several electroen-33 cephalographic signals measured simultaneously from an 34 individual's scalp during a particular task. Each signal could 35 be analyzed separately, and those with the most activity 36 would indicate an area of relative activation. However, var-37 ious signals can show simultaneous activation, revealing 38 communication between different areas of the brain during 39 the task (Engel & Singer, 2001;Fries, 2005). Furthermore, 40 different types of such coherence -or synchrony -may 41 be evident for different mental processes, as is the case with 42 epileptic seizures (Quian Quiroga et al., 2002). Thus, the 43 study of synchrony and oscillatory systems can provide a 44 valuable means of studying psychophysiological processes, 45 as well as possible changes in those processes as a function 46 of different stimuli and conditions. 47In the current study we propose the application of two 48 recently-developed methodologies for examining the rela-49 tions between two time series. The first technique is the 50 Empirical Mode Decomposition (EMD), an algorithm for 51 filtering continuous time series data. The second method is 52 the structural heteroscedastic measurement-error (SHME) 53 model, which is adapted here for detecting linear associa-54 tions between two discrete time series. We apply these tech-55 niques to physiological data from individuals in couples that 56 participated in a laboratory-based social interaction task. 57 The paper is organized as follows. First, we provide a 58 brief review of some of the common synchronization mea-59 sures and their rationale in the context of emotional pro-60 cesses in dyadic interactions. Second, we describe the 61 EMD and SHME methods, with details about each of the 62 required steps for their implementation. Third, we illustrate 63 the application of the proposed methods with an application. 64 The paper ends with a discussion of the potential of these 65 models in psychophysiological research. of large values of this measure occurring during each task. For heart rate, which is output discretely, we use a structural error on both series. The results of this study indicate that these methods are in detecting synchrony between physiological measures and can be used to examine emotional coherence in dyadic interactions. s, dynamical systems, psychophysiologyThe synchronization of oscillatory systems -or coupled The synchronization of oscillatory systems -or coupled oscillations ...

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Methodological Advances for Detecting Physiological Synchrony During Dyadic Interactions

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“…Hence the null hypothesis would also be rejected for the female data. We may therefore further suspect the suitability to these data of any measurement error model which involves an equation error component, as such models produce slope estimates very close to those obtained using OLS (as in Kulathinal, et al 2002) and Patriota, et al 2009). …”

Section: A Test For Misspecification Of a Linear Model For Real Datamentioning

confidence: 92%

A Dynamic Test for Misspecification of a Linear Model

McAssey¹,

Hsieh²

2011

Nonparametric Statistical Methods and Related Topics

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Various linear models may be specified when attempting to estimate an apparent linear trend in real data sets, based on assumptions about the possibly unknown mechanism for generating the data. However, in many cases the best-fit line obtained from implementation of the specified model does not agree at all with the apparent trend in a scatterplot of the data, based on the evident geometric structure. We use both real and simulated data to illustrate the consequences of misspecifying a particular linear model for situations in which that model is inappropriate, and propose a dynamic test which may be used to determine when its specification is appropriate. Introduction: Modeling the linear trend in real bivariate dataThe World Health Organization (WHO) established the Multinational MONItoring of trends and determinants of CArdiovascular disease (MON-ICA) during the 1980s to study the association between known risk factors, like smoking and obesity, and trends in cardiovascular disease. The linear association between data on the average annual change in the observed risk score (X) and the average annual change in event rate (Y ), both given as percentages, should be modeled using a measurement error structure, with the sampling error in the statistics taken as the heteroscedastic measurement error (Kulathinal, et al. (2002)). However, whether or not we account for the measurement error, we obtain about the same estimate of the slope of this linear trend when the specified model includes an addi- The additive equation error component ε i is a (usually Gaussian) random variable with mean zero and variance σ 2 , with ε 1 , . . . , ε n independent.If one examines either data scatterplot and uses raw intuition-based on the apparent geometry of the data scatter-to project the location of the line which most suitably captures the linear association between the two variables, rather than using mathematical rigor, he would likely conclude that the slope of the plotted best-fit line based on the SLM is significantly smaller than the projected slope. A similar best-fit line is obtained when the measurement error is incorporated into the model using approaches whose structures are akin to that of the SLM. This apparent underestimation of the slope occurs because specification of the SLM for these data fails to capture the underlying mechanism which generated the data.Since the data-generation mechanism which produced the geometric structure of the data cloud is often unknown, an investigator who wishes to derive reliable estimates for a linear trend in the data requires simple but effective tools to determine the most appropriate model for that trend among those available. In this paper, we propose such a tool and demonstrate its implementation for identifying when a proposed linear model is inappropriate. While the examples presented here involve misspecification of the SLM, this dynamic test is intended as a tool for identifying misspecification of any linear model. Illustration: Slope underestimation with the SLMTo furthe...

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“…In other words, we consider the models (1) and (2) with q i being identically zero. For the interval estimation/hypothesis testing of the equation-error model, interested readers may refer to de Castro, Galea, and Bolfarine [3] and Patriota, Bolfarine, and de Castro [4].…”

Section: Introductionmentioning

confidence: 99%