Function implements Kernel-Based Regularized Least Squares (KRLS), a machine learning method described in Hainmueller and Hazlett (2014) that allows users to solve regression and classification problems without manual specification search and strong functional form assumptions. KRLS finds the best fitting function by minimizing a Tikhonov regularization problem with a squared loss, using Gaussian Kernels as radial basis functions. KRLS reduces misspecification bias since it learns the functional form from the data. Yet, it nevertheless allows for interpretability and inference in ways similar to ordinary regression models. In particular, KRLS provides closed-form estimates for the predicted values, variances, and the pointwise partial derivatives that characterize the marginal effects of each independent variable at each data point in the covariate space. The distribution of pointwise marginal effects can be used to examine effect heterogeneity and or interactions.
● Data Source:
CranContrib
● Keywords:
● Alias: krls
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Internal function that computes choice coefficients for KRLS given a fixed value for lambda (the parameter that governs the tradeoff between model fit and complexity in KRLS). This function is called internally by krls. It would normally not be called by the user directly.
● Data Source:
CranContrib
● Keywords:
● Alias: solveforc
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Internal function that computes Leave-On-Out (LOO) Error for KRLS given a fixed value for lambda (the parameter that governs the tradeoff between model fit and complexity in KRLS). This function is called internally by krls to find value of lambda that minimizes the LOO error. It would normally not be called by the user directly.
● Data Source:
CranContrib
● Keywords:
● Alias: looloss
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Internal function that is called by krls to computes first differences for binary predictors in the X matrix. It would normally not be called by the user directly.
● Data Source:
CranContrib
● Keywords:
● Alias: fdskrls
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Summarizes average partial derivatives (i.e. marginal effects) and the distribution of the partial derivatives for each predictor. For binary predictors, the marginal effects are the first differences if krls(,derivatives=TRUE,binary=TRUE) was specified.
● Data Source:
CranContrib
● Keywords:
● Alias: summary.krls
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Function conducts leave-one-out optimization to find lambda using a golden search search with caching. This function is called internally by krls. It would normally not be called by the user directly.
● Data Source:
CranContrib
● Keywords:
● Alias: lambdasearch
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Produces two types of plots. The first type of plot shows histograms for the pointwise partial derivatives to examine the heterogeneity in the marginal effects of each predictor (which==1). The second type of plot shows estimates of the conditional expectation functions of E[Y|X] for each predictor (which==2). For each plot, the predictor of interest varies from its 1st to its 3rd quartile values, while the other predictors are kept at the means (or other values specified in setx). For binary varibales the E[Y|X] are predicted at the max and the min value of the predictor (instead of the range from the 1st to the 3rd quantile).
● Data Source:
CranContrib
● Keywords:
● Alias: plot.krls
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Predicted values and standard errors based on krls model object.
● Data Source:
CranContrib
● Keywords:
● Alias: predict.krls
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Given a N by D numeric data matrix, this function computes the N by N distance matrix with the pairwise distances between the rows of the data matrix as measured by a Gaussian Kernel.
● Data Source:
CranContrib
● Keywords:
● Alias: gausskernel
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providing 
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