# Sub-sampling a dataset

## Introduction

Some subtle issues can arise here. This chapter attempts to explain the issues.

A sub-sample may be defined in relation to a full data set in two different ways: we will refer to these as setting the sample and restricting the sample respectively.

## Setting the sample

By setting the sample we mean defining a sub-sample simply by means of adjusting the starting and/or ending point of the current sample range. This is likely to be most relevant for time-series data. For example, one has quarterly data from 1960:1 to 2003:4, and one wants to run a regression using only data from the 1970s. A suitable command is then

    	smpl 1970:1 1979:4

Or one wishes to set aside a block of observations at the end of the data period for out-of-sample forecasting. In that case one might do

    	smpl ; 2000:4

where the semicolon is shorthand for leave the starting observation unchanged. (The semicolon may also be used in place of the second parameter, to mean that the ending observation should be unchanged.) By unchanged here, we mean unchanged relative to the last `smpl` setting, or relative to the full dataset if no sub-sample has been defined up to this point. For example, after

    	smpl 1970:1 2003:4
    	smpl ; 2000:4

the sample range will be 1970:1 to 2000:4.

An incremental or relative form of setting the sample range is also supported. In this case a relative offset should be given, in the form of a signed integer (or a semicolon to indicate no change), for both the starting and ending point. For example

    	smpl +1 ;

will advance the starting observation by one while preserving the ending observation, and

    	smpl +2 -1

will both advance the starting observation by two and retard the ending observation by one.

An important feature of setting the sample as described above is that it necessarily results in the selection of a subset of observations that are contiguous in the full dataset. The structure of the dataset is therefore unaffected (for example, if it is a quarterly time series before setting the sample, it remains a quarterly time series afterwards).

## Restricting the sample

By restricting the sample we mean selecting observations on the basis of some Boolean (logical) criterion, or by means of a random number generator. This is likely to be most relevant for cross-sectional or panel data.

Suppose we have data on a cross-section of individuals, recording their gender, income and other characteristics. We wish to select for analysis only the women. If we have a `gender` dummy variable with value 1 for men and 0 for women we could do

    	smpl gender=0 --restrict

to this effect. Or suppose we want to restrict the sample to respondents with incomes over $50,000. Then we could use

    	smpl income>50000 --restrict

A question arises here. If we issue the two commands above in sequence, what do we end up with in our sub-sample: all cases with income over 50000, or just women with income over 50000? By default, in a gretl script, the answer is the latter: women with income over 50000. The second restriction augments the first, or in other words the final restriction is the logical product of the new restriction and any restriction that is already in place.

If you want a new restriction to replace any existing restrictions you can first recreate the full dataset using

          smpl full

Alternatively, you can add the `replace` option to the `smpl` command:

          smpl income>50000 --restrict --replace

This option has the effect of automatically re-establishing the full dataset before applying the new restriction.

Unlike a simple setting of the sample, restricting the sample may result in selection of non-contiguous observations from the full data set. It may also change the structure of the data set.

This can be seen in the case of panel data. Say we have a panel of five firms (indexed by the variable `firm`) observed in each of several years (identified by the variable `year`). Then the restriction

    	smpl year=1995 --restrict

produces a dataset that is not a panel, but a cross-section for the year 1995. Similarly

    	smpl firm=3 --restrict

produces a time-series dataset for firm number 3.

For these reasons (possible non-contiguity in the observations, possible change in the structure of the data), gretl acts differently when you restrict the sample as opposed to simply setting it. In the case of setting, the program merely records the starting and ending observations and uses these as parameters to the various commands calling for the estimation of models, the computation of statistics, and so on. In the case of restriction, the program makes a reduced copy of the dataset and by default treats this reduced copy as a simple, undated cross-section. With one exception: if you start with a balanced panel dataset and the restriction is such that it preserves a balanced panel — for example, it results in the deletion of all the observations for one cross-sectional unit — then the reduced dataset is still, by default, treated as a panel. If you wish to re-impose a time-series or panel interpretation of the reduced dataset you can do so using the command, or the GUI menu item Sample, Dataset structure.

The fact that restricting the sample results in the creation of a reduced copy of the original dataset may raise an issue when the dataset is very large (say, several thousands of observations). With such a dataset in memory, the creation of a copy may lead to a situation where the computer runs low on memory for calculating regression results. You can work around this as follows:

1. Open the full data set, and impose the sample restriction.

2. Save a copy of the reduced data set to disk.

3. Close the full dataset and open the reduced one.

4. Proceed with your analysis.

## Random sampling

With very large datasets (or perhaps to study the properties of an estimator) you may wish to draw a random sample from the full dataset. This can be done using, for example,

    	smpl 100 --random

to select 100 cases. If you want the sample to be reproducible, you should set the seed for the random number generator first, using .

This sort of sampling falls under the restriction category: a reduced copy of the dataset is made.

## The Sample menu items

The discussion above has focused on the script command . You can also use the items under the Sample menu in the GUI program to select a sub-sample.

The menu items mostly work in the same way as the corresponding `smpl` variant, except that when you use the item Sample, Restrict based on criterion, and the dataset is already sub-sampled, you are given the option of preserving or replacing the current restriction. Replacing the current restriction means, in effect, invoking the `replace` option described above ().