The Log Likelihood Ratio in Segmented Regression

Feder, Paul I.

doi:10.1214/aos/1176343000

Cited by 153 publications

(71 citation statements)

References 14 publications

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“…Hudson (1966) provides a graphic algorithm (for minimization of overall sum of squares of error, SSE, in the segmented model) and shows that the algorithm generally provides the maximum likelihood estimate (MLE) of the abscissa of an unknown breakpoint (tBP); he provides no information as to how likely that estimate may be (rendering inferences impossible). Feder (1975a;1975b) proves that, provided the model is identified (i.e. includes no more hypothesized breakpoints than are present in the real population), and if no hypothesized tBP coincides with an abscissa of observation in the sample, then minimization of SSE (the MLE function) converges asymptotically to the true population breakpoint (BP).…”

Section: Death Phasementioning

confidence: 94%

Survival of Bacterial Indicator-Species on Environmental Impervious Surfaces

Wilson

Pitt

2013

JWMM

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Because of historic difficulties in the measurement of sewage borne pathogens, the microbiological quality of stormwater runoff is often characterized on the basis of bacterial indicator species. These species are assumed to derive from a common (sewage) source with pathogens of interest, and to arrive in, survive in, and move through watershed environments in numbers that correlate with the health risk from those pathogens. Commonly used indicator species (especially Escherichia coli and Enterococcus spp., or enterococci), however, may derive from sources other than sewage, and survive in the (nonenteric) environment at rates divergent from those of the pathogens they are presumed to indicate (National Research Council, 2004).Field and Samadpour (2007) provide a critical review of both the the indicator paradigm (our current reliance on fecal indicator bacteria, FIBs) and an alternative monitoring regimen utilizing fecal source tracking (FST) methods. While noting the inadequate state of the art for direct measurements of pathogens, the authors find deficiencies in the correlations of FIBs to specific pathogens, and of FIBs to epidemiological measures of human health. They ascribe the deficiencies in the indicator paradigm to its inability to identify the source hosts of environmental FIBs. Landscape survival of FIBs and the ratio of FIBs to human pathogens deposited on the landscape are dependent on the source of the feces. More specifically, though zoonotic infections from non-human sources occur, correlation between human health threat and FIB presence suffers when major fecal sources other than sewage are present. (The

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Section: Death Phasementioning

confidence: 94%

Survival of Bacterial Indicator-Species on Environmental Impervious Surfaces

Wilson

Pitt

2013

JWMM

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“…Application of these joint locations to a linear model provides insight into the non-constant relationship of the data series (Muggeo 2003). Advanced practices in segmented regression analysis typically look beyond these independent models in an attempt to integrate a generalized theory (Hudson 1966;Farley and Hinich 1970;Kimeldorf and Wahba 1970;Feder 1975). However, this analysis is mathematically complex and partially ill-suited for direct application to the overall needs of this research (Feder 1975).…”

Section: Segmented Regression Analysismentioning

confidence: 99%

Product Life Cycle of the Manufactured Home Industry

Wherry¹,

Buehlmann

2014

BioResources

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“…The second statistic has the form n * In [SSE(HO) / SSE(Hl)]. This statistic has the -same asymptotic distribution as the first (Feder, 1975b). The corresponding F statistics and their descriptive significance levels are also printed.…”

Section: Investigating Hypothesesmentioning

confidence: 99%

“…The statistics appropriate for such tests are difficult to compute and converge rather slowly to their asymptotic distribution (e.g., Feder, 1975b). Segcurve optionally computes and writes to a file statistics that can be used to test for a one-phase model versus a wider class of alternative models.…”

Section: Investigating Hypothesesmentioning

confidence: 99%

A program for fitting two-phase segmented-curve models with an unknown change point, with an application to the analysis of strategy shifts in a cognitive task

Beem

1995

Behavior Research Methods, Instruments, & Computers

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A program is describedforfitting a regression model in which the relationship between the dependent and the independent variables is described by two regression equaThe last decade has seen substantial interest in the application of cognitive-process models of task performance to the analysis and description of individual differences in performance (see Lohman & Ippel, 1993;Snow & Lohman, 1993). One ofthe determinants of task performance that has emerged from these investigations is the strategy-shift phenomenon, whereby a subject may apply different strategies for solving different items of the same task. Studies that have identified strategies employed by subjects have used a variety of measures, including retrospective reports, eye-fixation records, errors, and measures of response latencies (e.g., Cooper, 1980;Glushko & Cooper, 1978;Kyllonen, Lohman, & Snow, 1984;Snow, 1980). Kyllonen, Lohman, and Woltz (1984) systematically studied subjects' strategy shifts on different items of the same spatial task as a function of item characteristics. They fitted several regression models for all subjects in order to identify the strategies that subjects used and the possible strategy shifts that occurred. Each model postulated different processes underlying performance, and some models postulated strategy shifts (of different Requests for reprints should be sent to A. L. Beem, Centre for the Study of Education and Instruction, Leiden University, Wassenaarseweg 52, P.O. Box 9555, 2300 RB Leiden, The Netherlands (e-mail: beem@rulfsw.leidenuniv.nl). kinds). The strategy-shift models were fitted with a few different shift points that were fixed a priori and that were the same for all subjects, rather than being estimated from each subject's data separately. The best-fitting process model for each subject was determined by comparing adjusted R-square statistics from different models. The results suggested not only that different subjects use different strategies, but also that the same subjects may use different strategies on different items of the same task, as well as that subjects differ in the point at which they shift from one strategy to another.Ippel and Beem (1987) fitted latencies of subjects on a mental-rotation task. In mental-rotation tasks, subjects must determine whether two figures are the same in shape or are mirror images. The figures can differ in orientation. Latencies typically suggest that subjects mentally rotate one of the figures into congruence with the other. On each trial, rotation can be achieved by either a clockwise or a counterclockwise routine. Depending on the angular disparity ofthe figures, one ofthese routines is objectively the most efficient, whereas 180 0 of angular disparity is an objectively optimal point for shifting from one rotation routine to the other. Ippel and Beem fitted subjects' latencies as a linear function of angular disparity with a model for which the shift point was not assumed to be known a priori, but was estimated from each subject's data separately. Latencies' lin...

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The Log Likelihood Ratio in Segmented Regression

Cited by 153 publications

References 14 publications

Survival of Bacterial Indicator-Species on Environmental Impervious Surfaces

Survival of Bacterial Indicator-Species on Environmental Impervious Surfaces

Product Life Cycle of the Manufactured Home Industry

A program for fitting two-phase segmented-curve models with an unknown change point, with an application to the analysis of strategy shifts in a cognitive task

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