我应该如何解释 R 中函数 multinom 的结果？

Question

I have a dataset with five categorical variables. And I ran a multinomial logistic regression with the function multinom in package nnet, and then derived the p values from the coefficients. But I do not know how to interpret the results.

The p values were derived according to UCLA's tutorial: https://stats.idre.ucla.edu/r/dae/multinomial-logistic-regression/ .

Just like this:

z <- summary(test)$coefficients/summary(test)$standard.errors
p <- (1 - pnorm(abs(z), 0, 1)) * 2
p

And I got this:

                        (Intercept)       Age1 Age2         Age3         Age4 Unit1      Unit2 Unit3 Unit4     Unit5    Level1    Level2     Area1     Area2
Not severe              0.7388029 9.094373e-01    0 0.000000e+00 0.000000e+00     0 0.75159758     0     0 0.0000000 0.8977727 0.9333862 0.6285447 0.4457171
Very severe             0.0000000 1.218272e-09    0 6.599380e-06 7.811761e-04     0 0.00000000     0     0 0.0000000 0.7658748 0.6209889 0.0000000 0.0000000
Severe                  0.0000000 8.744405e-08    0 1.052835e-06 3.299770e-04     0 0.00000000     0     0 0.0000000 0.8843606 0.4862364 0.0000000 0.0000000
Just so so              0.0000000 1.685045e-07    0 5.507560e-03 2.973261e-06     0 0.08427447     0   NaN 0.3010429 0.5552963 0.7291180 0.0000000 0.0000000
Not severe at all       0.0000000 0.000000e+00    0 0.000000e+00 0.000000e+00     0        NaN   NaN     0 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000

But how should I interpret these p values? Age3 is significantly related to Very severe? I am green to statistics and have no idea. Help me understand the results please. Thank you in advance.

Answer 1

I suggest using stargazer package to display coefficients and p-values (I believe that it is a more convenient and common way)

Regarding the interpretation of the results, in a multinomial model you can say: keeping all other variables constant, if Age3 is higher by one unit, the log odds for Very Severe relative to the reference category is higher/lower by that amount indicated by the value of the coefficient. The p-value just shows you whether the association between these two variables (predictor and response) is significant or not. Interpretation is the same that of other models.

Note: in case of p-value the null hypothesis is always that the coefficient is equal to zero (no effect at all). When p-value is less than 0.05, you can safely reject the null hypothesis and state that the predictor has an effect on the response variable.

I hope I could give you some hints