![]() The lengths of the lines reflect the size of the coefficient, i.e. how dramatic the change is. So our coefficients \(j\) tell us the change in slope for the data from the previous section of data defined by the knots. 3 our decreasing trend is lessening ( line). The fourth coefficient is positive, which means that between. 2 ( line), the coefficient is negative again, furthering the already decreasing slope (i.e. steeper downward). We have a decreasing function starting from that point onward ( line). In the plot above, the initial dot represents the global constant ( \(\gamma_1\), i.e. our intercept). The following uses the data we employed for demonstration before. Here our polynomial spline will be done with degree \(l\) equal to 1, which means that we are just fitting a linear regression between knots. With link function \(g(.)\), model matrix \(X\) of \(n\) rows and \(p\) features (plus a column for the intercept), a vector of \(p\) coefficients \(\beta\), we can write a GLM as follows:įor the GAM, it could look something like: ![]() The number of knots and where to put themĪs we noted before, a GAM is a GLM whose linear predictor includes a sum of smooth functions of covariates.
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