# Datasets¶

## General Datasets¶

Here, the choice set of interest $$X=\{x_1,\ldots,x_m\}$$ consists of finitely many general/unstructured alternatives, and the available data is a collection of menus of such alternatives and the observed choices at these menus. Formally, a menu is a set $$A\subseteq X$$, and the observed choice(s) at this menu is (are) captured by the set $$C(A)$$, where $$\emptyset\subseteq C(A)\subseteq A$$.

A general dataset

$\mathcal{D}=\left\{\big(A_i,C(A_i)\bigr)\right\}_{i=1}^k$

is a collection of $$k$$ observations, with each of them a pair of a menu and the alternative(s) chosen from it (if any). In particular, if $$C(A)$$ contains more than one alternative for some menu $$A$$ in $$\mathcal{D}$$, it is understood that the decision maker has chosen (or may be thought of as having chosen) any or all these alternatives at $$A$$, possibly over different instances where $$A$$ was presented in $$\mathcal{D}$$ (see also merging). If $$C(A)=\emptyset$$, then it is understood that the decision maker has chosen the no-choice/outside option, hence to avoid or defer choice at menu $$A$$.

It is also possible that the data available to the analyst features a default/status quo option, reflecting situations where the decision maker was initially endowed with some alternative $$s\in A$$ before asked to choose from menu $$A$$.

A general dataset with default/status quo alternatives

$\mathcal{D}=\left\{\big((A_i,s_i),C(A_i,s_i)\bigr)\right\}_{i=1}^k$

is a collection of $$k$$ observations, with each of them a pair comprising a decision problem and the alternative(s) that was/were observed to be chosen at this decision problem. In each decision problem $$(A_i,s_i)$$, $$A_i$$ is a menu and $$s_i\in A_i$$ the default/status quo alternative at that menu, while $$\emptyset\neq C(A_i,s_i)\subseteq A_i$$ is required to hold for all $$i\leq k$$ in such datasets.

Tip

To be analyzable by Prest v0.9.11, a general dataset must be a .csv file.

To import such a dataset into Prest, select “Workspace -> Import general dataset” and select the target file from the relevant directory.

The new pop-up window features four column headers under “Columns”: Subject, Menu, Default and Choice. Select the appropriate column name in your .csv file from the drop-down menu to match the corresponding column header. If your dataset does not feature default alternatives, select “None” for the Default header.

To view the imported dataset in Prest, double-click on it in the workspace area.

## Budgetary Datasets¶

Here, consumer behavior with respect to $$n$$ commodities is analyzed when data is available on the prices of these commodities, captured by a vector $$p\in\mathbb{R}^n_{+}$$, and also on consumer demand at these prices, captured by a vector/consumption bundle $$x\in\mathbb{R}^n_+$$.

A budgetary dataset

$\mathcal{D}=\left\{(p^i,x^i)\right\}_{i=1}^k$

is a collection of $$k$$ observations, with each of them a pair $$(p^i,x^i)$$ comprising the consumption bundle $$x^i$$ that was observed to be chosen when prices were $$p^i$$.

Tip

To be analyzable by Prest v0.9.11, a budgetary dataset must be a .csv file.

To import such a dataset, go to “Workspace -> Import budgetary dataset” and select the target file from the relevant directory.

Budgetary datasets with $$n$$ goods must have the following structure:

• Column 1: subject ID
• Column 2: price of good 1
• Column $$n+1$$: price of good $$n$$
• Column $$n+2$$: demand of good 1
• Column $$2n+1$$: demand of good $$n$$

To view the imported dataset, double-click on it in the workspace area. An extra column with the total expenditure associated with each observation is automatically added.