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Model selection is the task of selecting a model from among various candidates on the basis of performance criterion to choose the best one. [1] In the context of machine learning and more generally statistical analysis , this may be the selection of a statistical model from a set of candidate models, given data.
Matching is a statistical technique that evaluates the effect of a treatment by comparing the treated and the non-treated units in an observational study or quasi-experiment (i.e. when the treatment is not randomly assigned).
To apply AIC in practice, we start with a set of candidate models, and then find the models' corresponding AIC values. There will almost always be information lost due to using a candidate model to represent the "true model," i.e. the process that generated the data.
Similarly, for a regression analysis, an analyst would report the coefficient of determination (R 2) and the model equation instead of the model's p-value. However, proponents of estimation statistics warn against reporting only a few numbers. Rather, it is advised to analyze and present data using data visualization.
The clearest case is where precision is taken to be mean squared error, say = + in terms of squared bias and variance for the estimator associated with model . FIC formulae are then available in a variety of situations, both for handling parametric , semiparametric and nonparametric situations, involving separate estimation of squared bias and ...
"Best linear unbiased estimation and prediction under a selection model". Biometrics. 31 (2): 423– 447. doi:10.2307/2529430. JSTOR 2529430. PMID 1174616. Liu, Xu-Qing; Rong, Jian-Ying; Liu, Xiu-Ying (2008). "Best linear unbiased prediction for linear combinations in general mixed linear models". Journal of Multivariate Analysis. 99 (8): 1503 ...
PSM has been shown to increase model "imbalance, inefficiency, model dependence, and bias," which is not the case with most other matching methods. [3] The insights behind the use of matching still hold but should be applied with other matching methods; propensity scores also have other productive uses in weighting and doubly robust estimation.
The BIC is formally defined as [3] [a] = (^). where ^ = the maximized value of the likelihood function of the model , i.e. ^ = (^,), where {^} are the parameter values that maximize the likelihood function and is the observed data;