This page explains how you do logistic regression with Praat. You start by saving a table in a text file (if it contains non-ASCII symbols such as æ or ɛ, use the UTF-8 or UTF-16 format). The following example contains natural stimuli (female speaker) with measured F1 and duration values, and the responses of a certain listener who is presented each stimulus 10 times.

```
F1 Dur /æ/ /ɛ/
```

```
764 87 2 8
```

```
674 104 3 7
```

```
574 126 0 10
```

```
566 93 1 9
```

```
618 118 1 9
```

```
1025 147 10 0
```

```
722 117 7 3
```

```
696 169 9 1
```

```
1024 124 10 0
```

```
752 92 6 4
```

In this table we see 10 different stimuli, each characterized by a certain combination of the factors (independent variables) *F1* (first formant in Hertz) and *Dur* (duration in milliseconds). The first row of the table means that there was a stimulus with an F1 of 764 Hz and a duration of 87 ms, and that the listener responded to this stimulus 2 times with the response category /æ/, and the remaining 8 times with the category /ɛ/.

A table as above can be typed into a text file. The columns can be separated with spaces and/or tab stops. The file can be read into Praat with **Read Table from table file...**. The command **To logistic regression...** will become available in the **Statistics** menu.

###
What does it do?

The logistic regression method will find values *α*, *β*_{F1} and *β*_{dur} that optimize

*α* + *β*_{F1} *F1*_{k} + *β*_{dur} *Dur*_{k} = ln (*p*_{k}(/ɛ/)/*p*_{k}(/æ/)) |

where *k* runs from 1 to 10, and *p*_{k}(/æ/) + *p*_{k}(/ɛ/) = 1.

The optimization criterion is *maximum likelihood*, i.e. those *α*, *β*_{F1} and *β*_{dur} will be chosen that lead to values for *p*_{k}(/æ/) and *p*_{k}(/ɛ/) that make the observations in the table most likely.

Praat will create an object of type **LogisticRegression** in the list. When you then click the **Info** button, Praat will write the values of *α* (the *intercept*), *β*_{F1} and *β*_{dur} into the Info window (as well as much other information).

The number of factors does not have to be 2; it can be 1 or more. The number of dependent categories is always 2.

### Links to this page

© ppgb, October 1, 2014