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I have a question about glm model fitting of my data. The distribution shape is likely to follow a poisson distribution, but the response variable is not count/rate, but continuous decimals with both positive an negative values (as shown below).

enter image description here

There are only a few family types for me to choose in the glm(): binomial(link = "logit") gaussian(link = "identity") Gamma(link = "inverse") inverse.gaussian(link = "1/mu^2") poisson(link = "log") quasi(link = "identity", variance = "constant") quasibinomial(link = "logit") quasipoisson(link = "log")

Could you please give me some suggestions that which one should be more appropriate to my case?

Thanks in advance for your attention and help!

Best

LE

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    $\begingroup$ Regular OLS regression only assumes that the DV is continuous, not anything about its shape. It assumes that the error (as measured by the residual) is normal. $\endgroup$ – Peter Flom Feb 12 '14 at 14:35
  • $\begingroup$ OK! Thank you very much! I am not sure whether a Gaussian distribution is appropriate for this case. Should I try to fit a Gaussian model and exam the variances? @PeterFlom $\endgroup$ – user26221 Feb 12 '14 at 15:21
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    $\begingroup$ First fit an OLS model, then examine the residuals. In R you can get nice plots of the model by something like (pseudo code): m1 <- lm(DV~IV) plot(m1) $\endgroup$ – Peter Flom Feb 12 '14 at 15:34
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    $\begingroup$ To extent @PeterFlom's point, you've presented the unconditional sample distribution of the response but for GLMs (and regression models), the distributional assumption is conditional (that is, at a given combination of the independent variables, the distribution hold). Depending on the arrangement of the various x-variables, the marginal response might look quite different from the conditional one. [Also, why do you say the shape 'is likely to follow a Poisson distribution'? Since you also say it's continuous and can be negative, we can be quite certain it's not Poisson.] $\endgroup$ – Glen_b Feb 13 '14 at 23:40
  • $\begingroup$ Thanks you very much for your help! I am not familiar with the unconditional distribution so I cannot identify it. Could you please give me some suggestions to model the data. Since GLM is not appropriate, what kind of model can I try? @Glen_b $\endgroup$ – user26221 Feb 17 '14 at 13:46

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