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Lite form:

I'm trying to find the correct terminology to use to separate between "consider" parameters (included in the regression model, but held fixed and not estimated) and "solve-for" parameters (estimated by the regression model) with respect to regression analysis, and any guidance on implementing it. I've been googling for an hour, but i can't find any solid references to what I'm referring to, nor any definitively better terminology for it.

Long form:

I'm working on code to perform a non-linear least squares regression on a data set, with SVD as the backbone solution. Any of the parameters i'm performing the regression for should be able to be set to one of three modes: Estimate (solve for), Consider (factor into the regression, but don't change the value), or Ignore (not used in the regression model.). A covariance matrix and residuals are computed for all the non-ignored values. I'm trying to discern the correct terminology is.

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  • $\begingroup$ The parameters set as constant values are called constants. The parameters that are found by regression are called parameter values found by the regression of a model fit to data. $\endgroup$
    – Carl
    Aug 9, 2017 at 1:20
  • $\begingroup$ Perhaps you mean nuisance parameter, estimated parameter/ parameter to be estimated, constant, offset etc.? $\endgroup$
    – Björn
    Aug 9, 2017 at 6:01

1 Answer 1

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Q1 Estimate (solve for) $\leftarrow$ this terminology in not used. The calculated values of regression coefficients, i.e., parameter-values, are not generally called solutions because generally there are more $y$-values than there are $f(x)$ parameters leading typically to overdetermined systems of equations. Regressions are not solutions per se, but are approximate solutions.

Q2 Consider (factor into the regression, but don't change the value) One may call this the a priori assignment of parameter values. Sometimes, parameter values of restricted ranges are assigned because of prior knowledge. Sometimes, a fairly exact population parameter is known from prior research, which is then incorporated into a regression model rather than calculating that parameter as a statistic in the sample being analyzed. For example, we might know fairly exactly what the energy of transition is in a nuclear decay, so that may simplify calculating regression spatial frequency of ionizations resulting from interactions of the decay products with the environment.

Q3 or Ignore (not used in the regression model.) Ignore works, but it may be less confusing to use not include. For example, in a cubic fit, the square term may contribute nothing important to the regression, indeed its partial probability may be large, and its inclusion may decrease the adjusted R$^2$-value and/or F-statistic of an ANOVA regression model.

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