
Hi,



I'm a very new user of R and I hope not to be too "basic" (I tried to
find the answer to my questions by other ways but I was not able to).



I have 12 response variables (species growth rates) and two
environmental factors that I want to test to find out a possible
relation.

The sample size is quite small: (7<n<12, depending on each species-case).

I performed a Shapiro test (shapiro.test) to test for normal
distribution of the responses variables and they were normally
distribuited 10 times (over 12 possible, i.e. 12 response variables).

I performed a Generalized Linear Model in R-software (MASS package),
and I selected models by automatic backward stepwise (stepAIC
procedure) considering as the starting model the one with the additive
effects of both the factors. This is the case for six species growth
rates (six cases) but for the others six I tested the effect of just
one factor ("x2", see below) using just the "glm" procedure.



So, my object containing the data is called "data" and, this is the editor for the first species (sp1):

GLM1<-glm(growth.sp1~x1+x2,family=gaussian, data)

MOD.SELECTION<-stepAIC(GLM1, trace=TRUE) 

summary(MOD.SELECTION)



Here I attach an example of one of these analyses and after I finally
give you my questions (I hope not to be too long-winded!!):



> sp1.starting.model<-glm(sp1~x1+x2,family=gaussian, data)

> sp1.back<-stepAIC(sp1.starting.model, trace=TRUE)

Start:  AIC=63.6

sp1 ~ x1 + x2

       Df Deviance     AIC

- x2     1   73.490  61.801

<none>      72.278  63.602

- x1    1  122.659  67.949



Step:  AIC=61.8

gpf ~ x1



       Df Deviance     AIC

<none>      73.490  61.801

- x1    1  126.400  66.309

> summary(sp1.back)



Call:

glm(formula = sp1 ~ x1, family = gaussian, data = data)



Deviance Residuals: 

     Min        1Q    Median        3Q       Max  

-5.04833  -1.15233  -0.06802   0.81325   5.11464  



Coefficients:

            Estimate Std. Error t value Pr(>|t|)  

(Intercept) -7.62399    3.11127  -2.450   0.0342 *

x1           0.20595    0.07675   2.683   0.0230 *

---

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



(Dispersion parameter for gaussian family taken to be 7.348965)



    Null deviance: 126.40  on 11  degrees of freedom

Residual deviance:  73.49  on 10  degrees of freedom

  (1 observation deleted due to missingness)

AIC: 61.801



Number of Fisher Scoring iterations: 2





THE QUESTIONS:

1) Can I trust in the existence of such statistical relation? I mean: is there a way to know the power of this test in R?

2) I decided to use always "family=gaussian" because I have also
negative values in my response variable and I cannot manage it in a
different way. In fact I was not able to use as link function a
"negative binomial" as I previously did in SAS because of negative
values of response variable (as R "told" me when I tried)

3) How should I interpret the dispersion value R give me (in the case
reported it was "7.3")? I mean, what range of values (if it does exist)
I would expect to make the result reliable in the case of
"family=gaussian" (I'm not interested in prediction but just in finding
a statistical relation)?



Thank you very much in advance,

Best wishes
_________________________________________________________________


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