# 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! – kjetil b halvorsen Sep 18 '15 at 13:13
• Have a look at: stats.stackexchange.com/questions/168303/… – kjetil b halvorsen Sep 18 '15 at 13:15
• I have 90 observations – user2386786 Sep 18 '15 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! – kjetil b halvorsen Sep 18 '15 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. – Peter Flom Sep 18 '15 at 13:25