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I am currently carrying out an investigation to find if certain factors such as playing home or away or position of a footballer affects overall pass completion using logistic regression. I am using R to compute my data. In my current section in which I am trying to analyse uses the data of every player to convey a general conclusion to whether or not the position of a player affects the successfulness of pass completion.

so far I have computed:

test.logit <- glm( cbind(Total.Successful.Passes.All,Total.Unsuccessful.Passes.All) ~
                   as.factor(Position.Id), data=passes.data, family = "binomial")

summary(test.logit)

and my output was:

Coefficients:
                        Estimate Std. Error z value Pr(>|z|)    

(Intercept)              0.28482    0.01256   22.67   <2e-16 

as.factor(Position.Id)2  0.99768    0.01438   69.38   <2e-16 

as.factor(Position.Id)4  1.06679    0.01398   76.29   <2e-16 

as.factor(Position.Id)6  0.68090    0.01652   41.23   <2e-16 

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 32638  on 10269  degrees of freedom
Residual deviance: 26499  on 10266  degrees of freedom

AIC: 60422

Number of Fisher Scoring iterations: 4

the intercept is goalkeepers,position.Id 2 is for a defender, 4 = midfielder and 6 = striker

Is this a good set of results to come to a conclusion? and with the large deviances?

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    $\begingroup$ This doesn't feel like a programming question, but rather one about how to interpret the results of a logistic regression. As such, I think this is off topic for SO. I would suggest consulting a statistics textbook, or even better a statistician. $\endgroup$
    – joran
    Jan 15, 2013 at 15:58

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Based on

  1. Very small p-values (less than 2e-16)
  2. Large effect size estimations (log-odds ratios ranging from .68 to 1.06)
  3. Small standard errors (around .015)

All evidence indicates there is a significant effect of position on the probability of a successful pass.

Note that the size of the deviance isn't immediately interpretable as "large" or "small" (deviance is affected by the sample size, so there is no such thing as a "large deviance" without context).

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    $\begingroup$ Position.Id here is a categorical variable. Therefore, doesn't the estimate and p-values show significance only with relation to the reference (which is not shown in the post) (what I mean is that if the factors were re-levelled, you might get different p-values)? Also, how important is the ratio of residual df to residual deviance in a logistic regression? Could you please comment on it? Thank you! $\endgroup$
    – Arun
    Jan 15, 2013 at 16:11
  • $\begingroup$ thank you very much for your help, it is much appreciated $\endgroup$
    – user54511
    Jan 15, 2013 at 16:23
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    $\begingroup$ @Arun: Yes, they do show significance relative only to the reference level. Note that 2 and 4 are therefore very close together (though probably still far apart enough, given those standard deviations, to be statistically significant). The OP should try releveling the factors to check that. The residual deviance and null deviance mostly play into the question of how much of the variance this regressor explains (while there is no equivalent to R^2 in logistic regression, there are some "pseudo-R^2"'s that use these deviances. $\endgroup$
    – David Robinson
    Jan 15, 2013 at 16:49

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