### Example 18.2 Conditional Logit and Data Conversion

In this example, data are prepared for use by the MDCDATA statement. Sometimes, choice-specific information is stored in multiple variables. Since the MDC procedure requires multiple observations for each decision maker, you need to arrange the data so that there is an observation for each subject-alternative (individual-choice) combination. Simple binary choice data are obtained from Ben-Akiva and Lerman (1985). The following statements create the SAS data set:

```data travel;
length mode \$ 8;
input auto transit mode \$;
datalines;
52.9   4.4 Transit
4.1   28.5 Transit
4.1   86.9 Auto
56.2  31.6 Transit
51.8  20.2 Transit
0.2   91.2 Auto
27.6  79.7 Auto
89.9  2.2  Transit
41.5  24.5 Transit
95.0  43.5 Transit
99.1  8.4  Transit

... more lines ...

```

The travel time is stored in two variables, `auto` and `transit`. In addition, the chosen alternatives are stored in a character variable, `mode`. The choice variable, `mode`, is converted to a numeric variable, `decision`, since the MDC procedure supports only numeric variables. The following statements convert the original data set, `travel`, and estimate the binary logit model. The first 10 observations of a relevant subset of the new data set and the parameter estimates are displayed in Output 18.2.1 and Output 18.2.2, respectively.

```data new;
set travel;
retain id 0;
id+1;
/*-- create auto variable --*/
decision = (upcase(mode) = 'AUTO');
ttime = auto;
autodum = 1;
trandum = 0;
output;
/*-- create transit variable --*/
decision = (upcase(mode) = 'TRANSIT');
ttime = transit;
autodum = 0;
trandum = 1;
output;
run;
```
```proc print data=new(obs=10);
var decision autodum trandum ttime;
id id;
run;
```

Output 18.2.1: Converted Data

id decision autodum trandum ttime
1 0 1 0 52.9
1 1 0 1 4.4
2 0 1 0 4.1
2 1 0 1 28.5
3 1 1 0 4.1
3 0 0 1 86.9
4 0 1 0 56.2
4 1 0 1 31.6
5 0 1 0 51.8
5 1 0 1 20.2

The following statements perform the binary logit estimation:

```proc mdc data=new;
model decision = autodum ttime /
type=clogit
nchoice=2;
id id;
run;
```

Output 18.2.2: Binary Logit Estimation of Modal Choice Data

The MDC Procedure

Conditional Logit Estimates

Parameter Estimates
Parameter DF Estimate Standard
Error
t Value Approx
Pr > |t|
autodum 1 -0.2376 0.7505 -0.32 0.7516
ttime 1 -0.0531 0.0206 -2.57 0.0101

In order to handle more general cases, you can use the MDCDATA statement. Choice-specific dummy variables are generated and multiple observations for each individual are created. The following example converts the original data set `travel` by using the MDCDATA statement and performs conditional logit analysis. Interleaved data are output into the new data set `new3`. This data set has twice as many observations as the original `travel` data set.

```proc mdc data=travel;
mdcdata varlist( x1 = (auto transit) )
select=mode
id=id
alt=alternative
decvar=Decision / out=new3;
model decision = auto x1 /
nchoice=2
type=clogit;
id id;
run;
```

The first nine observations of the modified data set are shown in Output 18.2.3. The result of the preceding program is listed in Output 18.2.4.

Output 18.2.3: Transformed Model Choice Data

Obs MODE AUTO TRANSIT X1 ID ALTERNATIVE DECISION
1 TRANSIT 1 0 52.9 1 1 0
2 TRANSIT 0 1 4.4 1 2 1
3 TRANSIT 1 0 4.1 2 1 0
4 TRANSIT 0 1 28.5 2 2 1
5 AUTO 1 0 4.1 3 1 1
6 AUTO 0 1 86.9 3 2 0
7 TRANSIT 1 0 56.2 4 1 0
8 TRANSIT 0 1 31.6 4 2 1
9 TRANSIT 1 0 51.8 5 1 0

Output 18.2.4: Results Using MDCDATA Statement

The MDC Procedure

Conditional Logit Estimates

Parameter Estimates
Parameter DF Estimate Standard
Error
t Value Approx
Pr > |t|
AUTO 1 -0.2376 0.7505 -0.32 0.7516
X1 1 -0.0531 0.0206 -2.57 0.0101