Solved – Interpretation of plotted component smooth functions of generalized additive model – transformed variables

data transformationdata visualizationgeneralized-additive-model

I have a plot of a GAM which models deforestation severity.

Component smooth functions of a GAM

The explanatory variables are transformed, with log10, inverse, and square root. Is it meaningful to interpret a gradient like this: 'Deforestation severity increases as log10(Distance to forest edge) increases' or 'Deforestation severity increases as distance to forest edge increases' for plot e (note, the lower the value of the y axis the greater the deforestation severity). If not, how could I plot the component smooth functions untransformed?

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You can transform the graph by changing trans in plot.gam(..., trans = I, ...) to something else instead of I, for example the inverses of the functions you mentioned.

HTH.

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Solved – Back-transformation and interpretation of $\log(X+1)$ estimates in multiple linear regression

According to Wooldridge 2009 (p. 192), the log(1 + x) transformation may retain the usual interpretation of log(x):

In cases where a variable $y$ is nonnegative but can take on the value 0, $log(1+y)$ is sometimes used. The percentage change interpretations are often closely preserved, except for changes beginning at $y=0$ (where the percentage change is not even defined). Generally, using $log(1+y)$ and then interpreting the estimates as if the variable were $log(y)$ is acceptable when the data contain relatively few zeros.

I suspect this extends to log2 or log10 bases.

Solved – Plotting gam model output – not component smooth functions

@Kate when I run your code, I get the following error from the last line, which is the key to the solution:

Error in eval(expr, envir, enclos) : object 'Loc' not found In addition: Warning message: In predict.gam(mod1, newdata = pred) : not all required variables have been supplied in newdata!

If you want to predict from a model, any model not just gam(), you must provide all the variables in the dataframe to predict from (the argument newdata).

pred <- data.frame(Doy = 1:365,  Tod=median(DatNew$Tod),
    Loc=factor('NewYork',levels=levels(DatNew$Loc)))
predict(mod1, newdata = pred)

And this works giving a predicted value of temperature for each day of the year in New York, assuming that they are measured at the median time of day. I tweaked your Doy values to be simply from 1 to 365, as presumably you only want one prediction for each day of the year. The value is almost completely flat because you simulated the data with no effect of Doy on temp, and it is almost exactly the expected value for a uniform(0,1) distribution, which is how you generated your random temperatures.

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Solved – Back-transformation and interpretation of $\log(X+1)$ estimates in multiple linear regression

Solved – Plotting gam model output – not component smooth functions

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