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One scenario is where all the parameters are estimated from the data; the other scenario is where a subset of the parameters is assumed known at their true values and the remaining parameters are estimated. We focus on quantities of interest which are defined on the scale of the response variable. We show that, under certain conditions, the ratio of a weighted sum across the design points of the variance of the quantity of interest is given by q\/p, where q and p are the number of free parameters in the two scenarios. Thus, in this average sense, the inflation in variance associated with adding parameters, also interpreted as the cost of adding parameters to a model, is directly proportional to the number of parameters. We study models involving power transformations, non-linear models and exponential family models.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1996.tb02103.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T07:09:54Z","timestamp":1544166594000},"page":"593-607","source":"Crossref","is-referenced-by-count":20,"title":["The Cost of Adding Parameters to a Model"],"prefix":"10.1093","volume":"58","author":[{"given":"Jeremy M. G.","family":"Taylor","sequence":"first","affiliation":[{"name":"University of California , Los Angeles , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arminda L.","family":"Siqueira","sequence":"additional","affiliation":[{"name":"Federal University of Minos Gerais , Belo Horizonte , Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert E.","family":"Weiss","sequence":"additional","affiliation":[{"name":"University of California , Los Angeles , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090921001712000_rssb02103-cit-0001","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1093\/biomet\/68.2.357","article-title":"On two families of transformations to additivity for binary response data","volume":"68","author":"Aranda-Ordaz","year":"1981","journal-title":"Biometrika"},{"key":"2024090921001712000_rssb02103-cit-0002","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316757","volume-title":"Nonlinear Regression Analysis and its Application.","author":"Bates","year":"1988"},{"key":"2024090921001712000_rssb02103-cit-0003","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1080\/01621459.1981.10477649","article-title":"An analysis of transformations revisited","volume":"76","author":"Bickel","year":"1981","journal-title":"J. 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