Ordinal logistic regression - How to handle NaNs

Question

I'm trying to run an ordinal logistic regression model with 5 IV's and a DV with 4 levels. I'm using the function polr from the MASS package in R. My data consists of 46 observations and all the IV's are continuous.

After fitting the model, I run the summary command, but I get the following warning: In sqrt(diag(vc)) : NaNs produced

After checking the variance-covariance matrix I find that the calculated variance for 3 of the IV's are negative (and very close to zero). Hence, R is only able to calculate SE's for 2 IV's. One of these IV's is significant with a p-value of roughly 0,008.

After reading some other threads, a possible explanation for the negative variance seems to be that the true variance of the beta is zero, or very close to zero. Is this a plausible explanation in a situation like this?

Nevertheless, I still have two question that I'm wondering about:

1. What would be a good approach for dealing with NaNs in a model like this (or in any type of regression model for that matter)? When I was a student in statistics I remember my teacher (it was a course on analysis of variance) telling us that one way of dealing with a negative variance would be to set it equal to zero, is that a reasonable approach here? That would however make it impossible to calculate a p-value, so I guess you would then assume the p-value to be basically zero as well?
2. Considering that my model produces NaNs, does that mean that the calculated p-values for my other two IV's are wrong or can I trust them? My guess is that the NaNs doesn't affect the two calculated SE's, but I am not very sure about this.

Any help with this would be very appreciated!

Model:

polr(DV ~ IV1 + IV2 + IV3 + IV4 + IV5, data = df, Hess=TRUE)

Data:

structure(list(DV = structure(c(1L, 2L, 3L, 4L, 4L, 3L, 3L, 2L, 
2L, 2L, 3L, 4L, 4L, 4L, 3L, 3L, 2L, 4L, 2L, 3L, 1L, 4L, 3L, 3L, 
3L, 1L, 4L, 2L, 3L, 4L, 3L, 3L, 2L, 3L, 3L, 2L, 4L, 2L, 4L, 3L, 
4L, 2L, 3L, 3L, 2L, 3L), .Label = c("1", "2", "3", "4"), class = "factor"), 
    IV1 = c(31.4471225882832, 26.7995926461918, 6.15597391098257, 
    32.2641357244643, 5.22243966268843, 50.905131621076, 15.9862670353658, 
    20.3080359821474, 8.65788372462158, 18.505603942379, 6.29152570809156, 
    24.9245052889569, 29.7359693719515, 21.859516176042, 22.8111791071324, 
    23.2948895757526, 7.48299489410315, 25.7653834495302, 11.4419627627679, 
    11.6797724921892, 18.9905104994504, 12.8525067743421, 23.7294286791083, 
    17.7572582793217, 6.51496922762868, 53.5047647614377, 19.7405021265905, 
    27.7157343854444, 20.2388180530257, 9.03173525976901, 15.3013141742333, 
    12.7120495663999, 15.7178643351835, 10.0053600142934, 16.6321423711387, 
    11.8383765639605, 11.4583741140051, 22.9047246959457, 7.72280996279261, 
    20.3566081932521, 7.17681029058905, 8.27263288950658, 27.9236215467482, 
    14.8812599466755, 11.9252118854612, 13.2169871327123), IV2 = c(5.60931899641577, 
    4.99118165784832, 5.40925266903915, 5.11764705882353, 4.89913544668588, 
    5, 5.07709251101322, 4.84575835475578, 3.73287671232877, 
    5.30413625304136, 5.52755905511811, 4.97975708502024, 5.02013422818792, 
    4.81481481481481, 4.69059405940594, 5.07853403141361, 4.31137724550898, 
    5.30913978494624, 4.73282442748092, 4.7065868263473, 5.18518518518519, 
    4.44909344490934, 4.55344070278185, 5.33557046979866, 5.37695590327169, 
    4.96981891348088, 4.60559796437659, 5.21172638436482, 5.10909090909091, 
    4.96318114874816, 5.19753086419753, 4.83164983164983, 4.62227912932138, 
    4.54188481675393, 4.79136690647482, 4.99156829679595, 4.67706013363029, 
    4.2027027027027, 4.81313703284258, 4.7979797979798, 4.29109159347553, 
    4.69798657718121, 4.48275862068965, 4.81012658227848, 4.86254295532646, 
    4.85776805251641), IV3 = c(18.4117647058824, 16.6470588235294, 
    17.8823529411765, 17.4, 18.8888888888889, 16.6875, 18.44, 
    18.85, 16.7692307692308, 19.8181818181818, 18.4736842105263, 
    17.5714285714286, 17, 17.6428571428571, 18.047619047619, 
    18.4761904761905, 16, 19.75, 18.0833333333333, 14.0357142857143, 
    18.1176470588235, 17.7222222222222, 16.3684210526316, 17.6666666666667, 
    18, 17.6428571428571, 16.4545454545455, 17.7777777777778, 
    16.5294117647059, 17.7368421052632, 18.304347826087, 15.9444444444444, 
    18.05, 17.35, 16.65, 17.4117647058824, 17.5, 14.8095238095238, 
    15.7407407407407, 16.7647058823529, 19, 17.5, 16.25, 12.6666666666667, 
    18.8666666666667, 16.4444444444444), IV4 = c(36.1498372555604, 
    29.4083258687817, 30.8237670147563, 30.6498598318535, 33.4609173395659, 
    33.8926923968973, 38.2607303267824, 35.6276276774419, 28.0350077556936, 
    29.8014773776547, 34.7520103344474, 34.2427136374588, 28.4133063999497, 
    30.8454122703714, 25.3434749682913, 31.7741243673625, 26.4398342610694, 
    30.0799370487075, 25.6232533845839, 22.8932982631499, 27.5351660757584, 
    40.9484363905134, 29.9603223354011, 41.4730169772058, 46.6645863988013, 
    25.463413385222, 38.0071453548843, 37.8674109498922, 25.1711130821037, 
    31.105850465851, 28.6739482669466, 33.4120721890402, 35.7158076753924, 
    29.1595387321196, 35.8018355105914, 33.826314306969, 31.3280107842738, 
    28.6294396753682, 26.8677745442452, 33.1564492854815, 23.3944257683981, 
    32.3845970978919, 21.6765100540051, 32.8688639919967, 29.5649229611823, 
    29.9880309522896), IV5 = c(4338.66666666667, 5806, 2450, 
    2624, 2259, 2831.5, 2879.66666666667, 4106.5, 4867, 8250, 
    3824.8, 3431, 1651.2, 2902.25, 3118, 1857.66666666667, 8377.2, 
    2022.33333333333, 4010, 5754.6, 5641, 4042.25, 5745.4, 5008.5, 
    6145.5, 3233.5, 2007.6, 2475.75, 1884.25, 6938.25, 3475, 
    6575.83333333333, 5564, 5474.8, 5665.75, 6787.66666666667, 
    3560.14285714286, 5707.4, 6354.25, 6548.75, 6883.66666666667, 
    7444.5, 6051.33333333333, 2750.5, 4788, 7105.2)), row.names = c(NA, 
-46L), class = c("tbl_df", "tbl", "data.frame"))

Answer 1

Thank you for adding the data. I tried rstanarm::stan_polr only to find the coefficients of three of the five predictors to be 0.0. Then I thought of a scale effect and apparently the large values in IV5 are the problem:

> summary(df)
 DV          IV1              IV2             IV3             IV4             IV5      
 1: 3   Min.   : 5.222   Min.   :3.733   Min.   :12.67   Min.   :21.68   Min.   :1651  
 2:12   1st Qu.:11.446   1st Qu.:4.692   1st Qu.:16.65   1st Qu.:28.47   1st Qu.:2885  
 3:19   Median :16.309   Median :4.860   Median :17.61   Median :30.83   Median :4563  
 4:12   Mean   :18.254   Mean   :4.878   Mean   :17.35   Mean   :31.46   Mean   :4592  
        3rd Qu.:23.197   3rd Qu.:5.101   3rd Qu.:18.11   3rd Qu.:34.16   3rd Qu.:5990  
        Max.   :53.505   Max.   :5.609   Max.   :19.82   Max.   :46.66   Max.   :8377  

If you scale the values of IV5 the functions runs with no problems:

> summary(polr(DV ~ IV1 + IV2 + IV3 + IV4 + scale(IV5), data = df, Hess=TRUE))
Call:
polr(formula = DV ~ IV1 + IV2 + IV3 + IV4 + scale(IV5), data = df, 
    Hess = TRUE)

Coefficients:
              Value Std. Error t value
IV1        -0.06206    0.03176 -1.9539
IV2        -0.85094    1.02221 -0.8325
IV3        -0.08293    0.22607 -0.3668
IV4         0.02918    0.05853  0.4986
scale(IV5) -0.94037    0.32998 -2.8498

Intercepts:
    Value   Std. Error t value
1|2 -8.8255  4.9492    -1.7832
2|3 -6.6140  4.8206    -1.3720
3|4 -4.5695  4.7956    -0.9529

Residual Deviance: 104.1743 
AIC: 120.1743 

Simply dividing IV5 values by 1000 works as well:

> summary(polr(DV ~ IV1 + IV2 + IV3 + IV4 + I(IV5/1000), data = df, Hess=TRUE))
Call:
polr(formula = DV ~ IV1 + IV2 + IV3 + IV4 + I(IV5/1000), data = df, 
    Hess = TRUE)

Coefficients:
               Value Std. Error t value
IV1         -0.06205    0.03176 -1.9536
IV2         -0.84851    1.02206 -0.8302
IV3         -0.08289    0.22606 -0.3667
IV4          0.02918    0.05853  0.4985
I(IV5/1000) -0.49940    0.17530 -2.8488

Intercepts:
    Value    Std. Error t value 
1|2 -11.1059   5.2975    -2.0964
2|3  -8.8946   5.1598    -1.7238
3|4  -6.8500   5.1160    -1.3389

Residual Deviance: 104.1744 
AIC: 120.1744