Andy Hector
- Published in print:
- 2015
- Published Online:
- March 2015
- ISBN:
- 9780198729051
- eISBN:
- 9780191795855
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198729051.003.0008
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies, Ecology
This chapter revisits a regression analysis to explore the normal least squares assumption of approximately equal variance. It also considers some of the data transformations that can be used to ...
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This chapter revisits a regression analysis to explore the normal least squares assumption of approximately equal variance. It also considers some of the data transformations that can be used to achieve this. A linear regression of transformed data is compared with the generalized linear model equivalent that avoids transformation by using a link function and non-normal distributions. Generalized linear models based on maximum likelihood use a link function to model the mean (in this case a square-root link) and a variance function to model the variability (in this case the gamma distribution where the variance increases as the square of the mean). The Box–Cox family of transformations is explained in detail.Less
This chapter revisits a regression analysis to explore the normal least squares assumption of approximately equal variance. It also considers some of the data transformations that can be used to achieve this. A linear regression of transformed data is compared with the generalized linear model equivalent that avoids transformation by using a link function and non-normal distributions. Generalized linear models based on maximum likelihood use a link function to model the mean (in this case a square-root link) and a variance function to model the variability (in this case the gamma distribution where the variance increases as the square of the mean). The Box–Cox family of transformations is explained in detail.
David McDowall, Richard McCleary, and Bradley J. Bartos
- Published in print:
- 2019
- Published Online:
- February 2021
- ISBN:
- 9780190943943
- eISBN:
- 9780190943981
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190943943.001.0001
- Subject:
- Sociology, Social Research and Statistics
Interrupted Time Series Analysis develops a comprehensive set of models and methods for drawing causal inferences from time series. Example analyses of social, behavioural, and biomedical time series ...
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Interrupted Time Series Analysis develops a comprehensive set of models and methods for drawing causal inferences from time series. Example analyses of social, behavioural, and biomedical time series illustrate a general strategy for building AutoRegressive Integrated Moving Average (ARIMA) impact models. The classic Box-Jenkins-Tiao model-building strategy is supplemented with recent auxiliary tests for transformation, differencing and model selection. New developments, including Bayesian hypothesis testing and synthetic control group designs are described and their prospects for widespread adoption are discussed. Example analyses make optimal use of graphical illustrations. Mathematical methods used in the example analyses are explicated assuming only exposure to an introductory statistics course. Design and Analysis of Time Series Experiments (DATSE) and other appropriate authorities are cited for formal proofs. Forty completed example analyses are used to demonstrate the implications of model properties. The example analyses are suitable for use as problem sets for classrooms, workshops, and short-courses.Less
Interrupted Time Series Analysis develops a comprehensive set of models and methods for drawing causal inferences from time series. Example analyses of social, behavioural, and biomedical time series illustrate a general strategy for building AutoRegressive Integrated Moving Average (ARIMA) impact models. The classic Box-Jenkins-Tiao model-building strategy is supplemented with recent auxiliary tests for transformation, differencing and model selection. New developments, including Bayesian hypothesis testing and synthetic control group designs are described and their prospects for widespread adoption are discussed. Example analyses make optimal use of graphical illustrations. Mathematical methods used in the example analyses are explicated assuming only exposure to an introductory statistics course. Design and Analysis of Time Series Experiments (DATSE) and other appropriate authorities are cited for formal proofs. Forty completed example analyses are used to demonstrate the implications of model properties. The example analyses are suitable for use as problem sets for classrooms, workshops, and short-courses.
