GLM输出中缺少一级因子

Question

I'm creating a model to investigate main effects and interactions between the total no of sharks ~ Month + SST + Sex. When I create the model for this test, the output only shows SexMale and not Sexfemale.

I understand one predictor is the intercept which has been accounted for, but Sexfemale does not appear when modelled alongside SST. Is there something I am missing?

Answer 1

The output is correct. If you have a factor variable, glm always uses n-1 interactions. In your case sexFemale is the baseline and sexMale will only be used if the sex variable = Male

EDIT based on comment of op

I created a very small reproducible example.

data <- data.frame(sharks = c(2,4,6,8,1,3,5,7),
                   season = c("spring", "spring", "summer", "summer", "autumn","autumn", "winter", "winter"),
                   sst = c(23,24,26,26,24,22,20,20),
                   sex = c("F", "F", "M", "M", "F", "M", "F", "F"))

# basic glm model
glm_mod <- glm(sharks ~ . , data = data)

Coefficients:
  (Intercept)  seasonspring  seasonsummer  seasonwinter  sst  sexM  
    -47             3            -4            13         2     6 

Interpretation: the baseline for the model is the autumn season and female sex. In other words, if it is autumn and the shark(?) is female the number of sharks is -47 + 2 * the temperature .

baseline: autumn + female because they are the first levels of the factor.

glm formula:
-47 + 3 * spring + -4 * summer + 13 * winter + 2 * sst + 6 * M

glm model with interactions between season and sex:

# glm model with interactions
glm_mod_interact <- glm(sharks ~ sst + season:sex , data = data)

Coefficients:
  (Intercept)                sst  seasonautumn:sexF  seasonspring:sexF  seasonsummer:sexF  seasonwinter:sexF  seasonautumn:sexM  
-45                  2                 -2                  1                 NA                 11                  4  
seasonspring:sexM  seasonsummer:sexM  seasonwinter:sexM  
NA                 NA                 NA  

The NA's are there because there is no data in the example data.frame for these combinations. But here you have all the interactions between sex and season. Whether this is significant you will have to figure out.

glm_mod_interact formula:
-45 + 2 * sst + -2 * seasonautumn:sexF + 1 * seasonspring:sexF + etc..

My advise is to read openintro statistics chapter 7 and further, or better yet, Data Analysis Using Regression and Multilevel/Hierarchical Models by Andrew Gelman and Jennifer Hill