Unusual high Odds Ratio Values in multinomial logistic regression

I was following the procedure in a statistics textbook to run a multinomial logistic regresion using mlogit. However, the Odds Ratios calculated seemed too high for some of the variables (>1000). Can someone take a look at this and check wether I am doing everything correctly? The data can be downloaded from here. I prepared the data with the following commands:

#read in the data
#trasnform data into the correct form for mlogit
mlogitData<-mlogit.data(test,choice="Outcome",shape="wide")
#build model
MLogitFit<-mlogit(Outcome~1|V1+V2+V3+V4+V5+V6+V7+V8,reflevel=3,data=mlogitData)
#summary of the model
summary(MLogitFit)
#OddsRatios
data.frame(exp(MLogitFit$coefficients)) # confidence Interval of the odds Ratios exp(confint(MLogitFit))  The summary of mlogit gives me:  Call: mlogit(formula = Outcome ~ 1 | V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8, data = mlogitData, reflevel = 3, method = "nr", print.level = 0) Frequencies of alternatives: Z A B 0.43333 0.25556 0.31111 nr method 7 iterations, 0h:0m:0s g'(-H)^-1g = 1.56E-06 successive function values within tolerance limits Coefficients : Estimate Std. Error t-value Pr(>|t|) A:(intercept) -6.74640 5.97451 -1.1292 0.2588147 B:(intercept) -7.12401 4.50350 -1.5819 0.1136759 A:V1 3.65979 3.90808 0.9365 0.3490331 B:V1 4.24363 3.25687 1.3030 0.1925822 A:V2 -15.11554 6.92901 -2.1815 0.0291475 * B:V2 -4.88778 3.65249 -1.3382 0.1808302 A:V3 1.71465 6.57907 0.2606 0.7943839 B:V3 2.94335 3.96557 0.7422 0.4579497 A:V4 -1.70660 1.58849 -1.0744 0.2826633 B:V4 -1.67210 1.17575 -1.4222 0.1549820 A:V5 1.18494 1.60760 0.7371 0.4610682 B:V5 1.03084 1.25573 0.8209 0.4116971 A:V6 8.28902 2.51631 3.2941 0.0009873 *** B:V6 3.44578 1.91844 1.7961 0.0724727 . A:V7 -1.34395 2.67943 -0.5016 0.6159612 B:V7 1.04803 1.95147 0.5370 0.5912343 A:V8 -7.46263 4.12978 -1.8070 0.0707577 . B:V8 0.21861 2.13596 0.1023 0.9184810 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Log-Likelihood: -64.636 McFadden R^2: 0.33149 Likelihood ratio test : chisq = 64.1 (p.value = 1.0515e-07)  Running data.frame(exp(MLogitFit$coefficients)) to calculate the odds ratios gives:

              exp.MLogitFit.coefficients.
A:(intercept)                1.175103e-03
B:(intercept)                8.055280e-04
A:V1                         3.885310e+01
B:V1                         6.966040e+01
A:V2                         2.725226e-07
B:V2                         7.538147e-03
A:V3                         5.554743e+00
B:V3                         1.897938e+01
A:V4                         1.814819e-01
B:V4                         1.878524e-01
A:V5                         3.270504e+00
B:V5                         2.803423e+00
A:V6                         3.979917e+03
B:V6                         3.136764e+01
A:V7                         2.608125e-01
B:V7                         2.852036e+00
A:V8                         5.741439e-04
B:V8                         1.244345e+00


I obtained the confidence interavls with: exp(confint(MLogitFit)):

                     2.5 %       97.5 %
A:(intercept) 9.650816e-09 1.430830e+02
B:(intercept) 1.182216e-07 5.488637e+00
A:V1          1.831725e-02 8.241213e+04
B:V1          1.176881e-01 4.123248e+04
A:V2          3.446800e-13 2.154711e-01
B:V2          5.864847e-06 9.688857e+00
A:V3          1.394913e-05 2.211978e+06
B:V3          7.994348e-03 4.505896e+04
A:V4          8.066986e-03 4.082774e+00
B:V4          1.875058e-02 1.881996e+00
A:V5          1.400307e-01 7.638467e+01
B:V5          2.392271e-01 3.285238e+01
A:V6          2.870699e+01 5.517731e+05
B:V6          7.303065e-01 1.347282e+03
A:V7          1.366460e-03 4.978060e+01
B:V7          6.223884e-02 1.306918e+02
A:V8          1.752860e-07 1.880591e+00
B:V8          1.891518e-02 8.185990e+01


The predicted Probabilities are as following:

fitted(MLogitFit, outcome=FALSE)
Z            A          B
[1,] 0.2790108926 3.880184e-01 0.33297074
[2,] 0.5191458618 2.900625e-01 0.19079169
[3,] 0.7263001933 1.633014e-02 0.25736966
[4,] 0.8386056883 3.700203e-03 0.15769411
[5,] 0.8050365007 7.487290e-03 0.18747621
[6,] 0.7855655154 3.860347e-02 0.17583101
[7,] 0.7878404896 7.992930e-03 0.20416658
[8,] 0.8386056883 3.700203e-03 0.15769411
[9,] 0.7878404896 7.992930e-03 0.20416658
[10,] 0.4363708036 2.827104e-01 0.28091885
[11,] 0.6126060746 3.320075e-02 0.35419317
[12,] 0.0274357267 8.418204e-01 0.13074390
[13,] 0.1438998597 5.869087e-01 0.26919146
[14,] 0.1850027820 2.105586e-01 0.60443858
[15,] 0.8427092407 5.933393e-03 0.15135737
[16,] 0.1537160539 4.929905e-01 0.35329341
[17,] 0.0434283140 6.358897e-01 0.32068201
[18,] 0.1868202029 1.141679e-01 0.69901186
[19,] 0.3064594418 1.156597e-01 0.57788084
[20,] 0.5737141160 6.734724e-02 0.35893865
[21,] 0.5841338911 1.374758e-01 0.27839031
[22,] 0.0866451414 4.019366e-01 0.51141821
[23,] 0.2794060013 9.964607e-02 0.62094793
[24,] 0.0252343516 7.343045e-01 0.24046118
[25,] 0.1314775919 4.602643e-01 0.40825811
[26,] 0.0274357267 8.418204e-01 0.13074390
[27,] 0.1303195991 6.649645e-01 0.20471586
[28,] 0.2818251202 4.896734e-01 0.22850146
[29,] 0.0063990341 8.874618e-01 0.10613917
[30,] 0.0002408527 9.742025e-01 0.02555668
[31,] 0.0523052465 7.073015e-01 0.24039322
[32,] 0.3287956423 2.756959e-01 0.39550841
[33,] 0.0419093705 7.521689e-01 0.20592173
[34,] 0.0523052465 7.073015e-01 0.24039322
[35,] 0.3287956423 2.756959e-01 0.39550841
[36,] 0.0100998700 7.475180e-01 0.24238212
[37,] 0.1609808596 2.268570e-01 0.61216212
[38,] 0.0119603037 8.065964e-01 0.18144331
[39,] 0.0697132279 4.549378e-01 0.47534896
[40,] 0.5756435353 6.315652e-02 0.36119994
[41,] 0.4689676672 6.796615e-02 0.46306619
[42,] 0.2652679745 6.358962e-02 0.67114240
[43,] 0.7870195702 2.038999e-03 0.21094143
[44,] 0.6438437943 9.222002e-03 0.34693420
[45,] 0.7462282258 5.881047e-04 0.25318367
[46,] 0.3532662528 2.193975e-01 0.42733620
[47,] 0.9563852795 4.133754e-05 0.04357338
[48,] 0.9079031419 2.786314e-03 0.08931054
[49,] 0.0220230156 8.017508e-01 0.17622619
[50,] 0.2268852285 1.745210e-01 0.59859376
[51,] 0.2268852285 1.745210e-01 0.59859376
[52,] 0.0751929214 6.261548e-01 0.29865225
[53,] 0.9426667411 4.520877e-06 0.05732874
[54,] 0.0212631471 6.729961e-01 0.30574075
[55,] 0.0212631471 6.729961e-01 0.30574075
[56,] 0.9218535421 1.166953e-02 0.06647693
[57,] 0.6374868816 3.856300e-02 0.32395012
[58,] 0.2920703240 2.410709e-01 0.46685876
[59,] 0.7047942848 1.728601e-02 0.27791970
[60,] 0.1850395244 5.297673e-01 0.28519316
[61,] 0.4402296785 8.870861e-03 0.55089946
[62,] 0.6781988218 3.852569e-04 0.32141592
[63,] 0.9889453179 4.036588e-05 0.01101432
[64,] 0.1618635354 8.011851e-02 0.75801796
[65,] 0.3008372801 9.835522e-02 0.60080750
[66,] 0.0740319347 4.284039e-01 0.49756417
[67,] 0.5529727485 1.768537e-01 0.27017351
[68,] 0.7824740564 5.001713e-03 0.21252423
[69,] 0.5343045050 5.865850e-02 0.40703700
[70,] 0.4564647083 1.733995e-01 0.37013579
[71,] 0.4711837972 8.449081e-03 0.52036712
[72,] 0.9154349308 2.364316e-02 0.06092191
[73,] 0.1858643216 2.217595e-01 0.59237621
[74,] 0.3770813535 9.943397e-02 0.52348468
[75,] 0.8124141650 3.243679e-04 0.18726147
[76,] 0.3195206223 2.932236e-01 0.38725578
[77,] 0.8615871019 5.063299e-04 0.13790657
[78,] 0.8615871019 5.063299e-04 0.13790657
[79,] 0.8254986241 2.059378e-03 0.17244200
[80,] 0.1208591778 4.615235e-01 0.41761730
[81,] 0.0035765650 9.093754e-01 0.08704806
[82,] 0.7583239965 3.544345e-02 0.20623255
[83,] 0.8141948591 5.016280e-03 0.18078886
[84,] 0.1204323818 2.545405e-01 0.62502710
[85,] 0.9594950290 3.694056e-05 0.04046803
[86,] 0.6858228916 1.691396e-01 0.14503752
[87,] 0.8254986241 2.059378e-03 0.17244200
[88,] 0.8254986241 2.059378e-03 0.17244200
[89,] 0.2463233530 2.793410e-01 0.47433568
[90,] 0.5674338104 1.448538e-02 0.41808081


To assess multicolinearity I calculated the VIF statistic but using the a glm model of the same dataset.

fullmod<-glm(as.factor(Outcome)~.,data=test,family=binomial())
vif(fullmod)
V1       V2       V3       V4       V5       V6       V7       V8
1.789116 1.822252 2.216444 1.320244 1.821820 1.439183 1.512865 1.121805

• How many observations do you have? You can have separation, so some observations gets predicted probs zero or one. Then the coefficients get very large. It is quite common! Commented Sep 18, 2015 at 13:13
• Have a look at: stats.stackexchange.com/questions/168303/… Commented Sep 18, 2015 at 13:15
• I have 90 observations Commented Sep 18, 2015 at 13:17
• And many variables? You cpuld easily have separation. But there is an easy way to check it: calculate the predicted probabilities, if any is 0/1, you have separation. This is not really a problem, it means that you have good predictors! But, it could mean that the usual asymptotic theory on which inference often is based is untrustworthy! Commented Sep 18, 2015 at 13:22
• Look at the CI for the variable with high OR (A:V6). It's 2.87 to 55,177. That's a problem. Could be complete or quasicomplete separation or could be collinearity. Commented Sep 18, 2015 at 13:25