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
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.