### Introduction

In this tutorial, we will learn how to load all observations from

- All or a subset of the variables.
- With or without data transformations, such as
- Creating dummy variables.
- Reclassifying string variables to integer categories.
- Creating interaction terms.
`ln`

,`exp`

,`lag`

and more.

from a well-formed dataset. All sections below apply to any dataset that meets our definition of 'well-formed' which is explained below.

#### What files does this apply to?

Our definition of a well-formed dataset includes

- Comma-separated text files (
**CSV**) with headers in the first line of the file. **Excel**files (**XLS**,**XLSX**) with headers in the first row of the file.**GAUSS**datasets (**DAT**) and matrix files (**FMT**).**SAS**(**SAS7BCAT**,**SAS7BDAT**),**SPSS**(**POR**,**SAV**) and**Stata**(**DTA**) datasets.- HDF5 files (
**H5**) if the dataset contains an attribute called`headers`

which contains the variable names.

Regardless of the file type, each file must be organized as a consistent tabular dataset like the example below. Each row of the file must have the same number of columns and each column of the file must have the same number of rows.

Age,Height,Weight 29,61,134 44,74,191 32,70,223

#### What files does this not apply to?

This section does not apply to

- Text files delimited by a character other than a comma.
- CSV files without headers or with empty lines.
- Excel files without headers.

or files which have inconsistent numbers of rows, or columns.

// This dataset is NOT well-formed. // It has: // 1. Comments at the top of the file. // 2. Inconsistent numbers of columns per row. Age,Height,Weight 29,61,134 44,74,191,43,16 32,70,223

## Headers

The GAUSS function `getHeaders`

will return a string array containing all the variable names from a dataset. It takes only one input, the name of the dataset. The example below reads all of the variable names from the Stata dataset `auto2.dta`

which is located in the GAUSS examples directory.

```
// Create file name with full path to Stata dataset
fname = getGAUSSHome() $+ "examples/auto2.dta";
// Read the variable names from the dataset
h = getHeaders(fname);
// Print string array containing the dataset headers
print h;
```

will return

make price mpg rep78 headroom trunk weight length turn displacement gear_ratio foreign

## All variables

The GAUSS command `loadd`

can read variables from a dataset. To read all variables from a dataset you only need to pass one input, a string containing the name of the dataset. The example dataset, `binary.csv`

, contains four variables related to college admissions, `admit`

, `gre`

, `gpa`

, and `rank`

.

```
// Create file name with full path
fname = getGAUSSHome() $+ "examples/binary.csv";
// Read all 4 variables from the CSV file
X = loadd(fname);
// Print the first 5 rows of all columns of 'X'
print X[1:5,.];
```

will return

admit rank gpa rank 0.00 380.00 3.61 3.00 1.00 660.00 3.67 3.00 1.00 800.00 4.00 1.00 1.00 640.00 3.19 4.00 0.00 520.00 2.93 4.00

## A subset of variables

`loadd`

can accept an optional second argument which is a formula string. The formula string specifies which variables to load and which data transformations to perform. The following operators can be used in a formula string to load a subset of the variables from the dataset.

Operator | Description |
---|---|

. | The dot represents all variables. |

+ | The plus operator adds a variable. |

- | The minus operator removes a variable |

### Example: Load two variables by name

```
// Create file name with full path to the SAS dataset
fname = getGAUSSHome() $+ "examples/detroit.sas7bdat";
// Load 2 variables by name from the SAS dataset
X = loadd(fname, "unemployment + weekly_earn");
// Print the first 5 rows of all columns of 'X'
print X[1:5,.];
```

will return

unemployment weekly_earn 11.0 117.18 7.0 134.02 5.2 141.68 4.3 147.98 3.5 159.85

### Example: Load all variables except for one

`cancer.dat`

is an example GAUSS dataset located in the GAUSS examples directory. It contains five variables, `time`

, `histology`

, `stage`

, `count`

, and `risktime`

. The example below loads all of these variables, except for `stage`

.

```
// Create file name with full path
fname = getGAUSSHome() $+ "examples/cancer.dat";
// Load all but one variable from the GAUSS dataset
X = loadd(fname, ". -stage");
// Print the first 5 rows of all columns of 'X'
print X[1:5,.];
```

will return

time histology count risktime 1.00 1.00 9.00 157.00 1.00 2.00 5.00 77.00 1.00 3.00 1.00 21.00 2.00 1.00 2.00 139.00 2.00 2.00 2.00 68.00

## Categorical variables

Some data files, such as CSV files, do not contain information specifying the types of the variables in the files. In these cases, it is sometimes necessary to specify how a particular variable should be interpreted.

The following keywords can be used in a formula string to tell GAUSS which variables should be interpreted as categorical or string variables and to create dummy variables if desired.

Keyword | Description |
---|---|

factor | Create dummy variables from a categorical variable, or column of integers. |

cat | Load text data and create a categorical variable. |

str | Load text data and create a string variable. |

### Example: Integer variable to dummy variables

`housing.csv`

is an example dataset from the GAUSS examples directory. The variable `baths`

, represents the number of bathrooms in the home and contains the following unique values: 1, 2, 3, and 4.

The example code below loads the `baths`

variable unmodified for comparison. In the next step, the code tells `loadd`

to create dummy variables from the integer categories in the `baths`

variable by using the `factor`

keyword in the formula string.

```
// Create file name with full path
fname = getGAUSSHome() $+ "examples/housing.csv";
// Load the original categorical data
baths = loadd(fname, "baths");
// Load the categorical variable and create dummy vars
dmy = loadd(fname, "factor(baths)");
```

After the code above, the first 5 rows of `baths`

and `dmy`

will be equal to

baths baths_2 baths_3 baths_4 baths = 2 dmy = 1 0 0 1 0 0 0 2 1 0 0 2 1 0 0 3 0 1 0

As you can see above, the base case is set to the case when `baths`

equals one.

### Example: Text categorical variable to dummy variables

The example Excel file, `nba_ht_wt.xls`

, contains seven variables with different information about NBA basketball players. The `Pos`

variable represents the position played by the basketball player. The levels are `C`

, `F`

, and `G`

, which represent center, forward and guard.

The code below uses the `cat`

keyword in the formula string to tell `loadd`

to create a categorical variable from the text data. Then the code wraps the `factor`

keyword around the `cat`

keyword to load the data as a categorical column and convert to dummy variables in one step.

```
// Create file name with full path
fname = getGAUSSHome() $+ "examples/nba_ht_wt.xls";
// Load the string variable turn it
// into a categorical variable
position = loadd(fname, "cat(Pos)");
// Load the string variable turn it into a
// categorical variable and then a dummy variable
pos_dummy = loadd(fname, "factor(cat(Pos))");
```

below is a preview of the first five observations created by the above code:

Pos Pos_F Pos_G position = C pos_dummy = 0 0 G 0 1 G 0 1 F 1 0 F 1 0

This time, `C`

, is the base case.

### Combining keywords and operators

Both the `cat`

and `factor`

keywords can be combined with the `.`

, `+`

and `-`

operators. For example, the following statements would be legal.

```
fname = getGAUSSHome() $+ "examples/housing.csv";
X = loadd(fname, "price + factor(baths) + taxes");
fname = getGAUSSHome() $+ "examples/yarn.xlsx"
X = loadd(fname, "cat(amplitude) + cycles");
```

## Interaction effects

The `*`

and `:`

operators are used in formula strings to create interaction effects.

Operator | Description |
---|---|

* | Represents an interaction between two variables as well as the original variables. |

: | Represents only the interaction between the two specified variables. |

### Example: Interaction term

By default when an interaction term is specified in a formula string, the variables that form the interaction are also included. The example below will load 3 variables, `Height`

, `Weight`

, and the interaction term of `Height*Weight`

.

```
// Create file name with full path
fname = getGAUSSHome() $+ "examples/nba_ht_wt.xls";
// Load the variables 'Height' and 'Weight'
// then create a third variable which is the
// interaction between them
nba = loadd(fname, "Height*Weight");
// Print the first 5 rows of the 3 specified variables
print nba[1:5,.];
```

The code above will print the following output

Height Weight Height_Weight 83 260 21580 74 180 13320 77 215 16555 81 260 21060 81 235 19035

The name of the product of `Height`

and `Weight`

is not `Height*Weight`

, because if that variable name was included in another formula string it would indicate an interaction term instead of this variable.

GAUSS replaces invalid characters from variable names with underscores.

### Example: Interaction term alone

Usually, when we create an interaction term, we will also include the original variables. However, it is sometimes useful to load only the interaction variable. We can specify that we only want the interaction, by using the colon operator, `:`

, in the formula string as shown below.

```
// Create file name with full path
fname = getGAUSSHome() $+ "examples/nba_ht_wt.xls";
// Load only one variable, which is the
// interaction between 'Height' and 'Weight'
X = loadd(fname, "Height:Weight");
// Print the first 5 rows of the 1 specified variable
print X[1:5];
```

The code above will print the following output

Height_Weight 21580 13320 16555 21060 19035

## Data transformations

GAUSS allows you to transform your variables when loading, by using a procedure in a formula string.

### Example: Natural log

```
// Create file name with full path to Stata dataset
fname = getGAUSSHome() $+ "examples/auto2.dta";
// Load 'price' from 'auto2.dta' and perform
// natural log transform
ln_price = loadd(fname, "ln(price)");
// Print the first 5 rows of 'ln_price'
print ln_price[1:5];
```

The code above will return the following output.

ln_price_ 8.3185 8.4657 8.2425 8.4797 8.9653

The variable name was updated to represent the transformation with the parentheses replaced with underscores.

### Example: The first difference of the natural log

Now let's do something slightly more complicated. Suppose you want to compute the first difference of the natural log of the `price`

variable from the `auto2.dta`

dataset. GAUSS allows you to use any procedure in a formula string **as long as it takes a column vector as the only input and returns a column vector of the same size as the only output**.

So we will first create a procedure to compute the first difference of the natural log. We will call it `lnDiff`

. Then we can use it in our formula string, like this

```
// Define procedure to compute the first
// difference of the natural log of a variable
proc (1) = lnDiff(x);
local ln_x;
// Compute the natural log of the input
ln_x = ln(x);
// Compute the difference of the natural log
// and return the result
retp(ln_x - lag(ln_x));
endp;
// Create file name with full path to Stata dataset
fname = getGAUSSHome() $+ "examples/auto2.dta";
// Load the 'price' variable and call
// our 'lnDiff' procedure on it
X = loadd(fname, "lnDiff(price)");
// Print the first 5 observations
print X[1:5];
```

The code above will print the following output. Note that the first observation is a missing value since we lose one observation when computing the lag.

lnDiff_price_ . 0.1472 -0.2232 0.2372 0.4856

### Conclusion

In this tutorial, we have learned how to

- Load all or a subset of variables with the
`+`

,`-`

and`.`

operators. - Creating dummy variables with the
`factor`

keyword. - Reclassifying string variables to integer categories with the
`cat`

keyword. - Creating interaction terms with the
`*`

and`:`

operators. - Performing data transformations by using GAUSS procedures in formula strings.

from a well-formed, tabular dataset.