# Interpreting a GLM call in R [beginner]

I am currently doing academic research in a linguistic field. Unfortunately, I have never had any statistical education. I have been reading on statistics for beginners lately (e.g. 1, 2, 3, 4, and also here on SE 5), and I've had my hands full with R - but I still have difficulties understanding the output of a GML call.

Let's say that I have a dataset d that contains four columns: Variant - Region - Noun - Preposition

Variant is the main column, it contains either "elke" or "iedere" (two Dutch synonyms that can theoretically be used interchangeably). Region contains values "VL" or "NL" (designating regions where an utterance is heard, obviously), Noun can be zero or one as can Preposition.

I did an individual analysis of each factor with a chi test, but I'd like to do a multivariable test. From what I've read GLM should do the trick:

fit <- glm(Variant ~ Region + Nomen + Preposition,
data=d, family=binomial)


But the result R gives me kind-a overwhelms me:

Deviance Residuals:
Min       1Q   Median       3Q      Max
-1.6448  -1.1224   0.7735   0.8315   1.7384

Coefficients:
Estimate   Std. Error   z value   Pr(>|z|)
(Intercept)  -0.30011   0.08026      -3.739    0.000185 ***
RegionVL     -0.96155   0.05596      -17.183   < 2e-16 ***
Noun         0.16926    0.08147      2.077     0.037758 *
Preposition  1.18437    0.05058      23.415    < 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: 10195.2  on 7372  degrees of freedom
Residual deviance:  9205.6  on 7369  degrees of freedom
AIC: 9213.6

Number of Fisher Scoring iterations: 4


I'm experiencing a lot of turbulence trying to get my head around this. From what I can gather (please correct me if I'm wrong!):

RegionVL means that R decided to pick VL as value 1, and transformed Region into RegionVL.

Pr(>|z|) contains the p values (that have to be less than 0,05 to be significant. If they are not, the variable is of no influence whatsoever)

Estmiate tells us what influence each factor has on the choice between "ieder" en "elke". For instance, Preposition has a lot of positive influence (i.e. when Preposition=1, chances are very large that Variant=elke or iedere (but how do you know which one?)). Region then has a lot of negative influence, which tends to lead to the other variant.

I do not know what Std. Error is (standard deviation?) nor what the z value is, even though I assume it is a very frequent statistical term.

I read that AIC should be as low as possible and that the higher it gets, the lesser plausible your test can be. But what are the limits? And does that mean that my test is unusable?

I'm sorry for the many questions. I've been trying to break this down as well as I could, but I still don't manage to get my head into this. I never shined in mathematics (hence, linguistics!) so this all quite new to me.

• Possible duplicates or near-duplicates: post1, post2, post3, post4 -- and more ... post3 is basic (&for 1 predictor). Search for more. – Glen_b Dec 28 '14 at 22:30

You are correct about Region - given that Region is categorical, it gets dummy coded.

Pr(>|z|) does give p values, and 0.05 is a typical cut-off point for significance, but the rest of your statement in that paragraph is not correct.

Estimate is values to be plugged into the logistic regression equation; they are not very intuitive; more intuitive are odds ratios. You can get these by take e ^ estimate or you can have R give them to you (along with their confidence intervals) with

exp(cbind(OR = coef(fit), confint(fit)))


Standard error is (in simple terms) an estimate of how good the estimates are.

AIC is useful only for comparing two or more models, if this is the only model you are running, you can ignore it.

• Could you also tell me what z value is? And, more globally, it still isn't clear to me how I can deduct from this information what is relevant to the choice of Variant and what is not/less relevant. Was my explanation correct? Could you add to that? – Bram Vanroy Dec 28 '14 at 15:03
• z is a test statistic. It is a measure of how far your data are from what would be expected under the null. Relevance is going to depend on substantive expertise as well as statistical knowledge. – Peter Flom Dec 28 '14 at 15:23
• So basically, from this test alone one cannot read the influence of the factors on Variant? I thought that that is wat Estimate does? – Bram Vanroy Dec 28 '14 at 15:30
• Yes, it can do that. Look at the odds ratios and read about how to use them. But that's just the statistics. You then need to interpret them. Are they big? Compared to what? – Peter Flom Dec 28 '14 at 15:31