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I'm attempting logistic regression in R for a survey for 613 students. I'm looking to see if there is an association between my Dependent Variable (called 'BinaryShelter', coded as 0 or 1, signifying whether students took shelter during a tornado warning) and my 5 independent/predictor variables. My categorical IV's have anywhere from 3 to 11 distinct levels/categories within them. The other two IV's are binary coded as 0 or 1. The first 10 surveys and R output are given below:

    Survey  KSCat   WSCat   PlanHome    PlanWork    KLNKVulCat  BinaryShelter
    1       J       B       1           1           A           1
    2       A       B       1           0           NA          1
    3       B       B       1           1           C           1
    4       B       D       1           1           A           0
    5       B       D       1           1           A           1
    6       G       E       1           1           A           0
    7       A       A       1           1           B           1
    8       C       F       NA          1           C           0
    9       B       B       1           1           A           1
    10      C       B       0           0           NA          1



Call:
glm(formula = BinaryShelter ~ KSCat + WSCat + PlanHome + PlanWork + 
KLNKVulCat, family = binomial("logit"), data = mydata)

Deviance Residuals: 
Min       1Q   Median       3Q      Max  
-2.0583  -1.3564   0.7654   0.8475   1.6161  

Coefficients:
              Estimate   St. Error  z val   Pr(>|z|)  
(Intercept)    0.98471    0.43416   2.268   0.0233 *
KSCatB        -0.63288    0.34599  -1.829   0.0674 .
KSCatC        -0.14549    0.27880  -0.522   0.6018  
KSCatD         0.59855    1.12845   0.530   0.5958  
KSCatE        15.02995 1028.08167   0.015   0.9883  
KSCatF         0.61015    0.68399   0.892   0.3724  
KSCatG        -1.60723    1.54174  -1.042   0.2972  
KSCatH        -1.57777    1.26621  -1.246   0.2127  
KSCatI        -2.06763    1.18469  -1.745   0.0809 .
KSCatJ        -0.23560    0.65723  -0.358   0.7200  
WSCatB        -0.30231    0.28752  -1.051   0.2931  
WSCatC        -0.49467    1.26400  -0.391   0.6955  
WSCatD         0.52501    0.71082   0.739   0.4601  
WSCatE        -0.32153    0.63091  -0.510   0.6103  
WSCatF        -0.51699    0.74680  -0.692   0.4888  
WSCatG        -0.64820    0.39537  -1.639   0.1011  
WSCatH        -0.05866    0.89820  -0.065   0.9479  
WSCatI       -17.07156 1455.39758  -0.012   0.9906  
WSCatJ       -16.31078  662.38939  -0.025   0.9804  
PlanHome       0.27095    0.28121   0.964   0.3353  
PlanWork       0.24983    0.24190   1.033   0.3017  
KLNKVulCatB    0.17280    0.42353   0.408   0.6833  
KLNKVulCatC   -0.12551    0.24777  -0.507   0.6125  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 534.16  on 432  degrees of freedom
Residual deviance: 502.31  on 410  degrees of freedom
  (180 observations deleted due to missingness)
AIC: 548.31

Number of Fisher Scoring iterations: 14

> Anova(ShelterYorN, Test = "LR")
Analysis of Deviance Table (Type II tests)

Response: BinaryShelter
          LR Chisq Df Pr(>Chisq)
KSCat       13.3351  9     0.1480
WSCat       14.3789  9     0.1095
PlanHome     0.9160  1     0.3385
PlanWork     1.0583  1     0.3036
KLNKVulCat   0.7145  2     0.6996

My questions are:

1) Does a very large St. Deviation (like the one for KSCatE) indicate that I should not use that level of that categorical IV if I want the model to fit the data better? The ones that had such large St. Deviations were from small groups. Should I not include data from very small groups? For instance if only 2 or 3 people picked category 'E' for KSCat, should I exclude that data?

2) When using factors for my categorical data, or when adding in more than one IV, sometimes my beta coefficients flip signs. Does this mean I should test for interaction and then try to conduct some form of a PCA or jump straight to doing a PCA?

These next questions may be better asked on stack overflow, but I figured I'd give it a shot here:

3) I do not want a particular level of the categorical variables to be the reference level. I know that R automatically picks the reference level (A if letters, and the first one if numbers). As in the answer to this question (Significance of categorical predictor in logistic regression), I tried fitting the model without an intercept by adding - 1 to the formula to see all coefficients directly. But when I do this, the results only show the 'A' level of the first variable and none of the others. For example, I can see results for 'KSCatA' but not 'WSCatA' or 'KLNKVulCatA'.

4) How does R handle missing observations for logistic regression? For example survey #10 was missing the 'KLNKVulCat' Variable, but not any of the other IV's. Would R or any other statistical languages not use any of the information for this particular person, or just that particular variable?

Any help is greatly appreciated, thank you.

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closed as too broad by mkt, Michael Chernick, COOLSerdash, Peter Flom Aug 28 at 12:41

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.