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Nonparametric series regression
Stata 16's new npregress series command fits nonparametric series regressions that approximate the mean of the dependent variable using polynomials, B-splines, or splines of the covariates. This means that you do not need to specify any predetermined functional form. You specify only which covariates you wish to include in your model. For instance, type
. npregress series wineoutput rainfall temperature i.irrigation
Instead of reporting coefficients, npregress series reports effects, meaning average marginal effects for continuous variables and contrasts for categorical variables. The results might be that the average marginal effect of rainfall is 1 and the contrast for irrigation is 2. This contrast can be interpreted as the average treatment effect of irrigation.
Being a nonparametric regression, the unknown mean is approximated by a series function of the covariates. And yet we can still obtain the inferences that we could from a parametric model. We use margins. We could type
. margins irrigation, at(temperature=(40(5)90))
and obtain a table of the expected effect of having irrigation at temperatures of 40, 50, ..., 90 degrees. And we could graph the result using marginsplot.
Even more, npregress series can fit partially parametric (semiparametric) models.

We used a beta prior distribution in this example, but we could have chosen another prior distribution
that supports our prior knowledge. For the final analysis, it is important to consider a range of different
prior distributions and investigate the sensitivity of the results to the chosen priors.
For more details about this example, see Hoff (2009). Also see Beta-binomial model in
[BAYES] bayesmh for how to fit this model using bayesmh.
Bayesian versus frequentist analysis, or why Bayesian analysis?
Why use Bayesian analysis? Perhaps a better question is when to use Bayesian analysis and when
to use frequentist analysis. The answer to this question mainly lies in your research problem. You
should choose an analysis that answers your specific research questions. For example, if you are
interested in estimating the probability that the parameter of interest belongs to some prespecified
interval, you will need the Bayesian framework, because this probability cannot be estimated within
the frequentist framework. If you are interested in a repeated-sampling inference about your parameter,
the frequentist framework provides that.

anyvalue(), anymatch(), and anycount() are for categorical or other variables taking integer
values. If we define a subset of values specified by an integer numlist (see [U] 11.1.8 numlist),
anyvalue() extracts the subset, leaving every other value missing; anymatch() defines an indicator
variable (1 if in subset, 0 otherwise); and anycount() counts occurrences of the subset across a set
of variables. Therefore, with one variable, anymatch(varname) and anycount(varname) are
equivalent.
With the auto dataset, we can generate a variable containing the high values of rep78 and a
variable indicating whether rep78 has a high value:
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