I ran a glm regression with log link and gamma distribution for modeling impact of appropriate cancer care on costs. Covariates include age, race/ethnicity, location, tumor stage, tumor grade to name a few. With 'no appropriate care' and 'stage 1' as reference categories for appropriate care and tumor stage variables, respectively, I get beta estimates of 9.0663, 0.6953, 0.6669 for intercept, non-appropriate care' and 'stage 2 tumor', respectively. When I change the reference category for tumor stage to 'stage 2', I get beta estimates of 8.7319, 0.6953, and -0.3288 for intercept, non-appropriate care, and 'stage 1 tumor' respectively. Even though the beta estimates for the key independent variable and other covariates remain the same, the beta estimate for intercept changes everytime I change the reference values of certain variables. Why does this happen? Would this not change the finding for key indepedent variable everytime I change the reference group for any covariate? I would appreciate if you can help me with this and also guide with an appropriate reference. Thank you in advance.
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