Calcite | Level 5

## Inverse mills ratio when the dependent variable is not binary

Hello Everyone,

I need your help with the SAS codes. I need to use a Heckman selection model to correct for endogeneity. In the first stage of my Heckman model, the dependent variable is CEO expertise. Since there are three categories of CEO expertise in my context, the dependent variable (CEO_Expert) takes value either 0,1, or 2 (0 if the CEO is an accounting expert; 1 if a finance expert; and 2 if a sales expert). I don’t know how to obtain inverse mills ratio when the dependent variable is ternary. In the past instances when my dependent variable was a 1/0 dummy, I used proc qlim to obtain inverse mills ratio.

PROC QLIM data = First_Stage;

model Y1 = X1 X2 / DISCRETE;

OUTPUT out=Have mills;

RUN;

I have seen only examples of using inverse Mills ratio involving binary probit selection equation. I would really appreciate it if someone shared the code to obtain inverse mills ratio when the dependent variable is not binary.

Thanks,

Gokul

3 REPLIES 3
SAS Super FREQ

## Re: Inverse mills ratio when the dependent variable is not binary

Mills ratio
The inverse Mills ratio can be computed for censored or truncated continuous responses, binary discrete responses, and endogenous selection variables via the MILLS option in the OUTPUT statement of SAS/ETS PROC QLIM and SAS Viya PROC CQLIM.

Calcite | Level 5

## Re: Inverse mills ratio when the dependent variable is not binary

Thank you for replying to my post. Will you please share the code that I can use to get the inverse mills ratio when my dependent variable takes values 0,1, & 2? I am a novice and know only basic SAS codes.

Thanks,

Gokul

SAS Super FREQ

## Re: Inverse mills ratio when the dependent variable is not binary

Hello,

I will further check on Friday (23/06) but I don't think that's possible.

Your 0, 1 & 2 response is neither belonging to censored or truncated continuous responses, nor to binary discrete responses.

Is your 0, 1 & 2 response on a nominal scale or on an ordinal scale?

And does inverse Mills ratio exist for multinomial or ordinal response?

Maybe you need a One-vs-Rest or One-vs-One approach (resulting in multiple inverse Mills ratio's).

https://machinelearningmastery.com/one-vs-rest-and-one-vs-one-for-multi-class-classification

BR,

Koen

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