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| GAMs or GAMMs are used to fit and plot a combination of time varying functions such as polynomials to responses. More than one function can be used in the same model of a response with one function fitted to the response over one time period and another function used over another time period with the functions possibly linked at a single time point, known as a knot. | GAMs or GAMMs are used to fit and plot a combination of time varying functions such as polynomials to responses. GAMs allow fitting of a penalized regression spline to time predictors such as time since diagnosis. Use of a spline allows for investigation of more flexible relationships rather than simply assuming a straight line relationship. More than one function can be used in the same model of a response with one function fitted to the response over one time period and another function used over another time period with the functions possibly linked at a single time point, known as a knot. |
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| They can include interaction terms to compare curves across different groups (e.g. males and females) with R^2 used as a means of assessing the degree of fit (interpreted as in linear regression). GAMs and GAMMs can be fitted in R using the ''mgcv'' procedure. McKeown and Sneddon (2014) describe and illustrate the use of GAMs and GAMMs with accompanying R code using the ''mgcv'' procedure presented in the appendix to the paper. | They can also include the 'usual' linear regression predictors including interaction terms to compare curves across different groups (e.g. males and females) with R^2 used as a means of assessing the degree of fit (interpreted as in linear regression). The Akaike Information Criterion can be sued to compare model fits. A second order Akaike Information Criterion (AICc – see Sugiura 1978, Hurvich and Tsai 1991) which is recommended for comparing models when there are small sample sizes. GAMs and GAMMs can be fitted in R using the ''mgcv'' procedure. McKeown and Sneddon (2014) describe and illustrate the use of GAMs and GAMMs with accompanying R code using the ''mgcv'' procedure presented in the appendix to the paper. |
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Wood SN (2017) Generalized Additive Models: An Introduction with R (2nd edition). Chapman and Hall/CRC. |
Generalized Additive (Mixed) Models (GAM(M)) - an overview
GAMs or GAMMs are used to fit and plot a combination of time varying functions such as polynomials to responses. GAMs allow fitting of a penalized regression spline to time predictors such as time since diagnosis. Use of a spline allows for investigation of more flexible relationships rather than simply assuming a straight line relationship. More than one function can be used in the same model of a response with one function fitted to the response over one time period and another function used over another time period with the functions possibly linked at a single time point, known as a knot.
They can also include the 'usual' linear regression predictors including interaction terms to compare curves across different groups (e.g. males and females) with R^2 used as a means of assessing the degree of fit (interpreted as in linear regression). The Akaike Information Criterion can be sued to compare model fits. A second order Akaike Information Criterion (AICc – see Sugiura 1978, Hurvich and Tsai 1991) which is recommended for comparing models when there are small sample sizes. GAMs and GAMMs can be fitted in R using the mgcv procedure. McKeown and Sneddon (2014) describe and illustrate the use of GAMs and GAMMs with accompanying R code using the mgcv procedure presented in the appendix to the paper.
References
McKeown GJ and Sneddon I (2014) Modeling Continuous Self-Report Measures of Perceived Emotion Using Generalized Additive Mixed Models. Psychological Methods 19(1), 155-174.
Wood SN (2017) Generalized Additive Models: An Introduction with R (2nd
- edition). Chapman and Hall/CRC.