A generalized multivariate analysis of variance model useful especially for growth curve problems

Potthoff, Richard F.; Roy, Sasanka

doi:10.1093/biomet/51.3-4.313

Cited by 915 publications

(354 citation statements)

References 16 publications

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“…In this paper we will discuss residuals in the Growth Curve model due to Potthoff and Roy (1964). For more details we refer to yon Rosen (1994) where the results, via Edgeworth type expansions, are applied to a real d a t a set.…”

Section: Introductionmentioning

confidence: 99%

Residuals in the growth curve model

Rosen

1995

Ann Inst Stat Math

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A b s t r a c t .Residuals for the Growth Curve model will be discussed. In univariate linear models as well as the ordinary multivariate analysis of variance model residuals are based on the difference between the observations and the mean whereas for the Growth Curve model we have three different residuals all showing various aspects useful for validating analysis. For these residuals some basic properties are established.

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Section: Introductionmentioning

confidence: 99%

Residuals in the growth curve model

Rosen

1995

Ann Inst Stat Math

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“…Potthoff and Roy [29] published data of a dental study at the University of North Carolina Dental School on 11 girls and 16 boys at ages 8, 10, 12 and 14. Each measurement is the distance (in millimetres) between the centre of the pituitary and the pterygomaxillary fissure.…”

Section: Examplementioning

confidence: 99%

“…Figure 5 shows the related boxplots per age. An Boxplot of the dental data set of Potthoff and Roy [29].…”

Section: Examplementioning

confidence: 99%

Multiple Contrasts for Repeated Measures

Hasler

2013

The International Journal of Biostatistics

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This article addresses the problem of multiple contrast tests for repeated measures. Three procedures are described and compared by simulations concerning the familywise error type I. The procedure based on sandwich estimators seems to be most robust, except for all-pair comparisons.Keywords: repeated measures, multiple contrasts, sandwich estimator, multivariate t-distribution, familywise error type I *Corresponding author: Mario Hasler, Christian-Albrechts-University, Kiel, Germany, E-mail: hasler@email.uni-kiel.de IntroductionMultiple contrast tests (MCTs) and related simultaneous confidence intervals (SCIs) are well-known methods for testing and estimating linear functions of means called contrasts. A broad class of testing problems can be handled in specifying suitable contrast coefficients. The many-to-one comparison of Dunnett [1] is one of the most frequently applied and cited testing procedures today and it represents a simple example. Several treatments are compared with one control and tested for deviation. The all-pair comparison of Tukey [2], comparing all treatments against each other, is another very well-known example. Bretz [3] has formulated the trend test of Williams [4] as an approximate MCT. Here, the contrast coefficients depend in addition on the sample sizes of the treatment groups. Moreover, other problem-specific contrasts can be defined (see Nelson [5], Westfall [6] or Bretz et al. [7] for example). Furthermore, MCTs and SCIs can also be formulated for ratios of means (see Dilba et al. [8]) if conclusions about ratios -rather than differencesof means are of interest. This applies when relative changes are to be analyzed. Because correlations between the contrasts are involved by a joint distribution, MCTs exactly maintain the familywise error type I (FWE) over all contrasts. No further multiplicity adjustment is needed. SCIs (and adjusted p-values) are obtained for all hypotheses to be tested, complying with the guideline of the ICH [9]. Stepwise or gatekeeping procedures, for example, do not allow informative SCIs; see Strassburger and Bretz [10] and Guilbaud [11].MCTs and related SCIs are usually confined to normally distributed, homoscedastic and independent data with one primary endpoint. For the heteroscedastic case, Hasler and Hothorn [12] described a solution based on Games and Howell [13]. Konietschke et al. [14] presented a non-parametric version. Hasler and Hothorn [15,16] gave extensions for the case of multiple correlated endpoints. Unlike conventional MCTs, these approaches represent approximate solutions. They focus on situations where the usual assumptions are not fulfilled. Repeated measures also represent a situation where such an assumption is not met. For example, the means of several groups have to be compared simultaneously but the measurement values for these groups come from the same measurement objects (patients, plants, etc.), respectively. The groups are mostly according to time points but they can also represent different parts of the body, for ...

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“…For example, each sensor might have had 30 half-hour time points and one cluster had 20 sensors while the other had 30 sensors. The data generator [11][12] was validated with parameter estimates from Potthoff and Roy's data [13]. Table 1 presents partial local parameters generated by each sensor at level-1, to be transmitted to the cluster heads.…”

Section: ( )mentioning

confidence: 99%

A Bayesian Multilevel Modeling Approach for Data Query in Wireless Sensor Networks

Wang

Fang

Espy

et al. 2007

Computational Science – ICCS 2007

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Abstract. In power-limited Wireless Sensor Network (WSN), it is important to reduce the communication load in order to achieve energy savings. This paper applies a novel statistic method to estimate the parameters based on the realtime data measured by local sensors. Instead of transmitting large real-time data, we proposed to transmit the small amount of dynamic parameters by exploiting both temporal and spatial correlation within and between sensor clusters. The temporal correlation is built on the level-1 Bayesian model at each sensor to predict local readings. Each local sensor transmits their local parameters learned from historical measurement data to their cluster heads which account for the spatial correlation and summarize the regional parameters based on level-2 Bayesian model. Finally, the cluster heads transmit the regional parameters to the sink node. By utilizing this statistical method, the sink node can predict the sensor measurements within a specified period without directly communicating with local sensors. We show that this approach can dramatically reduce the amount of communication load in data query applications and achieve significant energy savings.

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A generalized multivariate analysis of variance model useful especially for growth curve problems

Cited by 915 publications

References 16 publications

Residuals in the growth curve model

Residuals in the growth curve model

Multiple Contrasts for Repeated Measures

A Bayesian Multilevel Modeling Approach for Data Query in Wireless Sensor Networks

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