REGRESI DENGAN RESPONS KUALITATIF

Tedy Herlambang

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# REGRESI DENGAN RESPONS KUALITATIF

## Ekonometrika Sesi 5

### Tedy Herlambang .small[ ]

[ bangtedy.github.io](https://bangtedy.github.io)

[ @t_hlb](https://twitter.com/t_hlb)

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# Pendahuluan

Dengan mempelajari modul 5, Anda diharapkan dapat secara umum mampu mengestimasi mengevaluasi hasil regresi respon kualitatif. Secara khusus Anda diharapkan mampu:

1. Mengestimasi dan mengevaluasi linear probability model (LPM) dengan metode OLS
2. Mengestimasi regresi respon kualitatif dengan menggunakan metode maximum likelihood 
3. Mengestimasi model logit
4. Mengestimasi model probit
5. Mengevaluasi kelayakan model regresi respon kualitatif metode maximum likelihood dengan menggunakan uji likelihood ratio test (LR)
6. Mengevaluasi uji signifikansi model regresi respon kualitatif metode maximum likelihood dengan menggunakan uji Z atau Wald

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# KB1: MODEL PROBABILITAS LINIER (LPM)
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# MODEL PROBABILITAS LINIER

- In economics, there are frequently cases in which the dependent variable is of a qualitative nature. 
- The dummy is being used in the left-hand side of the regression model.
- For example, the ratings of various goods from consumer surveys taking the form of strongly disagree, disagree, indifferent, agree, strongly agree.
  
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# One simplest possible model

- The decision to go out to work or not is affected by only one explanatory variable `$(X_{2i})$` – average wage rate
- The model is `$$Y_i = β_1 + β_2X_{2i} + u_i$$` 
- Since `$Y_i$` is a dummy variable, we can rewrite the model as: `$$D_i = β_1 + β_2X_{2i} + u_i$$`
  - where `$X_{2i}$` is the average of wage rate (a continuous variable); 
  - `$D_i$` is a dichotomous dummy deﬁned as
     + 1 if the ith individual is working
     + 0 if the ith individual is not working
     + `$u_i$` is the disturbance.
  
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# Problems with the linear probability model

- `$D_i$` is not bounded by the (0,1) range
- Non-normality and heteroskedasticity of the disturbances
- The coefficient of determination as a measure of overall fit

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# KB2: MODEL LOGIT
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# Model Logit

- In the LPM, the dependent variable `$D_i$`, which reﬂects the probability `$P_i$` can take any real value and is not limited to being in the correct range of probabilities – the (0,1) range.
- To resolve this problem:
  - Transform the dependent variable, `$D_i$`, into odds: the ratio of the probability of success to its complement (the probability of failure)
  
  $$ odds_i = \frac {P_i}{1-P_i}$$
  
  - Use a linear regression to obtain the logit model
- The logit model maps probabilities from the range (0,1) to the entire real line.

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# KB3: MODEL PROBIT
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# Model Probit

- The probit model is an alternative method of resolving the problem faced by the linear probability model of having values beyond the acceptable (0,1) range of probabilities.
- Use a sigmoid function similar to that of the logit model by using
the cumulative normal distribution, which by definition has an S-shape asymptotical to the (0,1) range.
- The logit and probit procedures are so closely related that they rarely produce results that are significantly different. 
- The probit model is seen to be more suitable than the logit model as most economic variables follow the normal distribution
  - Hence it is better to examine them through the cumulative normal distribution.

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Matur nuwun, find me at...

[ @t_hlb ](https://twitter.com/t_hlb)

[ bangtedy.github.io](https://bangtedy.github.io)