Still questions remain about modeling choices. The purpose of this study was to evaluate the performance of spatial only models in predicting national monthly exposure estimates of fine particulate matter at different time aggregations during the time period for the contiguous United States.
Additional goals were to evaluate the difference in prediction between federal reference monitors and non-reference monitors, assess regional differences, and compare with traditional methods. Using spatial generalized additive models GAM , national models for fine particulate matter were developed, incorporating geographical information systems GIS -derived covariates and meteorological variables.
Results were compared to nearest monitor and inverse distance weighting at different time aggregations and a comparison was made between the Federal Reference Method and all monitors. Cross-validation was used for model evaluation. Using all monitors, the cross-validated R2 was 0. The spatial GAM showed the weakest performance for the northwest region. In conclusion, National exposure estimates of fine particulates at different time aggregations can be significantly improved over traditional methods by using spatial GAMs that are relatively easy to produce.
It is clear that some features have a fairly simple linear relationship with the target variable. There are about three features that seem to have strong non-linear relationships though. We will want to combine the interpretability of these plots, and the power to prevent over fitting in GAMs to come up with a model that generalizes well to a holdout set of data.
Partial dependency plots are extremely useful because they are highly interpretable and easy to understand. For example at first examination we can tell that there is a very strong relationship between the mean radius of the tumor and the response variable.
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The bigger the radius of the tumor, the more likely it is to be malignant. Other features like the mean texture are harder to decipher, and we can already infer that we might want to make that a smoother line we walk through smoothing parameters in the next section. Tuning Smoothness and Penalties. This is where the functionality of pyGAM begins to really shine through. We can choose to build a grid for parameter tuning or we can use intuition and domain expertise to find optimal smoothing penalties for the model.
Main parameters to keep in mind are:. The default parameters that are being used in the model presented above are the following…. We change parameter list to the following: Note that another cool thing about pyGAM is that we can specify one single value of lambda and it will be copied to all of the functions. Otherwise, we can specify each one in a list…. Which changes our training accuracy to 0. And now the partial dependency plots look like so:.
The drop in accuracy tells us that there is some information we are not capturing by smoothing the mean texture estimator that much, but it highlights how the analyst can encode intuition into the modeling process.
Generalised additive models (GAMs): an introduction
Tuning these can be labor intensive, but there is an automated way to do this in pyGAM. Grid search with pyGAM. The gridsearch function creates a grid to search over smoothing parameters. This is one of the coolest functionalities in pyGAM because it is very easy to create a custom grid search.
One can easily add parameters and ranges. And just like the default argument is shows, we can add more and more arguments to the function and thus create a custom grid search. Generalizing a GAM. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account. If the address matches an existing account you will receive an email with instructions to retrieve your username. Search for more papers by this author. Tools Request permission Export citation Add to favorites Track citation. Share Give access Share full text access.
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