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I want to investigate the relationship between stock traders' past success rate (i.e. the number of total winning trades divided by the total trades executed) on the status of their current trading decision. The current trading decision is the dependent variable and is a categorical variable that takes the value of 1 if the trade is a win, -1 if it is a loss and 0 if the trader decides not to trade.

I am conducting a multinomial regression where the dependent variable is the current trade decision (1,-1,0) as mentioned above and the independent variable is the trader's historical success rate.

I choose a multinomial model rather than an ordinal model since, in my opinion, the 3 states are really independent. If the trader traded and made a profit of 0, then it would make sense to categorize the decision as an ordinal variable. But since trading (whether win or lose) is not the same as not trading then I argue that this should be a multinomial variable. Nevertheless, the relationship between win and lose is relative/ordinal. Is my reasoning correct here?

Given that no-trade is the baseline, I obtain the following results from the R output

enter image description here

I am not very clear on how to interpret the output in this case. I tried to follow the example here. The R output states that these are coefficient values and not log odds. Does this mean that a 1 unit increase in historical success rate increases the log odds of winning by 1.224 and decreases the log odds of losing by 0.622? Or are these coefficients? How should I interpret the results?

UPDATE: R results

Call:
multinom(formula = formula, data = data)

Coefficients:
  (Intercept)           Success Rate Cummulative_NumTrades
-1  -3.601953                 -0.622         -1.304052e-05
1   -4.660911                  1.224         -1.342798e-05

Std. Errors:
   (Intercept)           Success Rate Cummulative_NumTrades
-1 8.630168e-08           2.734970e-08          1.341129e-06
1  1.016195e-07           4.889536e-08          1.161023e-06

Residual Deviance: 392352.8 
AIC: 392376.8
finstats
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  • This is not raw R output so it's difficult to interpret it. It would help if you included the raw output produced by R as well as the R command(s) you used to obtain that output. We have no way of telling how you processed the output you provided, which can only lead to misguided interpretations. – Isabella Ghement Aug 02 '19 at 20:17
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    Possible duplicate of [Interpreting exp(B) in multinomial logistic regression](https://stats.stackexchange.com/questions/17196/interpreting-expb-in-multinomial-logistic-regression) and https://stats.stackexchange.com/questions/255046/coefficient-interpretation-in-multinomial-logistic-regression – rolando2 Aug 03 '19 at 00:40
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    @IsabellaGhement I have updated the question to include the R output. The output states that these are coefficients but in the link I posted, they say they are log odds. – finstats Aug 04 '19 at 16:22
  • I can't answer your question, @roland, as it was marked as duplicate. It looks like you are using the multinom() function to fit your multinomial model. The R output you showed doesn't match your description of the model - it should include only Success Rate as a predictor (?). – Isabella Ghement Aug 04 '19 at 21:01
  • In any event, if your model includes only Success Rate as a predictor, then you are fitting two models on the log-odds scale. The first model stipulates that the log odds that the current trading decision is a loss (-1) rather than a no trade decision change linearly with Success Rate. The second model stipulates that the log odds that the current trading decision is a win (+1) rather than a no trade decision change linearly with Success Rate. – Isabella Ghement Aug 04 '19 at 21:07
  • Usually, it is harder for people to interpret log odds so you can exponentiate the coefficients reported by multinom() to get odds ratios. – Isabella Ghement Aug 04 '19 at 21:10
  • If you exponentiate the coefficients reported by multinom(), then you can say things like: For each 1-unit increase in the value of Success Rate, the odds that the current trading decision is a loss (-1) rather than a no trade decision change by a multiplicative factor of exp(-0.622) = 0.54. You can compute (0.54 - 1)*100% = -46% and report a 46% decrease in these odds for each additional 1-unit increase in Success Rate. (This interpretation assumes only Success Rate is in your model.) – Isabella Ghement Aug 04 '19 at 21:21
  • The R output you provided seems to actually include 2 predictors: Success Rate and Cumulative Number of Trades. Is the latter predictor used as a denominator in the computation of Success Rate? If yes, your two predictors are "mathematically coupled" and you would have to be careful to the interpretational challenges this coupling would pose. – Isabella Ghement Aug 04 '19 at 21:24

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