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I need to fit a GLM (generalized linear model) in R, something like

model <- glm(Daily.Results ~ sqrt.of.Clicks + Days + log.of.Clicks * sqrt.of.Days, family = poisson)

which relates

Daily.Results = variable that I need to count (and predict)

Clicks = counts clicks in a link (which drives a person to be a potencial buyer)

sqrt.of.Clicks = square root of Clicks

log.of.Clicks = natural logarithm of Clicks

Days = 1, 2, 3... sqrt.of.Days = square root of 1, 2, 3...

in a dataset with 14 rows/observations

and family = poisson because Daily.Results are non negative integers, with log link-function

The results of summary(model) are:

Call:
glm(formula = Daily.Results ~ sqrt.of.Clicks + Days + log.of.Clicks * 
    sqrt.of.Days, family = "poisson")

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-2.24096  -0.61927  -0.09041   0.81640   2.45392

Coefficients:
                            Estimate Std. Error z value Pr(>|z|)    
(Intercept)                120.88890   22.33723   5.412 6.23e-08 ***
sqrt.of.Clicks               0.27487    0.07698   3.571 0.000356 ***
Days                         0.35892    0.09334   3.845 0.000120 ***
log.of.Clicks              -15.84863    3.20527  -4.945 7.63e-07 ***
sqrt.of.Days               -23.43680    4.22029  -5.553 2.80e-08 ***
log.of.Clicks:sqrt.of.Days   2.66063    0.47141   5.644 1.66e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 499.316  on 13  degrees of freedom
Residual deviance:  23.706  on  8  degrees of freedom
AIC: 141.81

Number of Fisher Scoring iterations: 4

The model above is the one which have the minimal AIC and Residual deviance (after some data transformation tentatives / log and sqrt of the data)

  1. I do not know very well how good or bad can be this model. By now, I often read people saying here that lower AIC and residual deviance means better fit. Is this correct and enough?
  2. Also, would be nice to know which value can be considered lower enough (R squared is so far more friendly). Can you help me with that?
  3. A really good fit can lead to bad predictions? Can you give some example?
  4. The diagnostic plots of my regression (plot(model)) follows, and I could not tell if some visual information can be found there. Perhaps, evidence of errors that I don't realized.

Residuals vs Fitted

Normal Q-Q

Scale-Location

Residuals vs Leverage

Cook's distance

Cook's distance vs Leverage

I think that a final and clean answer about this questions will help a lot of people here. Straight to the point.

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  • $\begingroup$ You have a large number of wide-ranging questions here. That doesn't lend itself to "a final and clean answer" that is "straight to the point". You might want to search the site & read a number of existing threads that overlap these topics. It may take a bit to get the information you want, but you would learn much in the process. Either way, you should probably trim this down to a single, answerable question. Then follow this up w/ a new question as the 1st is answered. You can always link back for context, if appropriate. $\endgroup$ – gung Apr 23 '18 at 19:45
  • $\begingroup$ @gung I looked already. But I'll try something else. $\endgroup$ – André Oliveira Apr 23 '18 at 19:50
  • $\begingroup$ Eg, for #3, you seem to be referring to overfitting, for #2 this might be helpful, here's a related search. Re #1, if people here already say this, what are you hoping for from the answer to this thread? What do you mean by "enough"? $\endgroup$ – gung Apr 23 '18 at 20:43
  • $\begingroup$ @gung Thanks for the links. I'll read carefully. About #1, I'll reformulate that later (if the question keeps unsolved). $\endgroup$ – André Oliveira Apr 23 '18 at 21:07
  • $\begingroup$ That's a good path forward, @Andre. I appreciate your being open minded about this. We'll see how it goes. $\endgroup$ – gung Apr 24 '18 at 0:48

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