Copyright: Copyright ¸ Kevin Lee


Contents

Overview

Getting Started

Usage

Main Menu and Toolbar

Linking Dialog Window

Technical Details

File Format

Model Selection

Integral Approximation

Parameterization


File Format

Input File Format

Column format

It requires every row to be read in the item parameter file is identical in terms of column format. For instance, if there are total 7 columns in each row and the 3rd column is the first element of a, 4th column is the second element of a,  6th column is d, 7th column is c, then the column format should be XXAAXDC. X means the read but unused column. Acceptable choices are X, A, B, C and D. All other will be treated as X.

For empirical theta files, the format is similarly something like XXTTXXX where T represents elements of theta and X is the unused column.

Row format

As for row selection, only unread rows need to be identified and empty row does not count. For instance, if rows 1, 3, 5 to 10 are to be skipped, the row skip format is {1,3,5-10}. Also {4S5} means skipping row 4-8. {4S2R1}, on the other hand, means to, starting at row 4, skip 2 rows (row 4 & 5), then read 1 row (row 6), then repeat the exact reading pattern (from row 7) till the end. A combination in any order, like {1,3-5,5S2, 8S1R3, 78-90}, is acceptable.

Output File Format

One example of the output file format is:

zfc101.par(1),zrc101.par(1),Ing:Grid[-4,4];W(0),T#:81,TD#:2,I#:40,M:1,P:2

4.089532e-02 0.80724 0.068636 -0.056156 0.839592 0.113839 -0.262078

*******************************************************************

Meaning of each line above:

1.	FROM file, TO file, (1) means 1.702 is multiplied to the exponent before the exponential function L[] is calculated; (0) means no such multiplication. Ing is the integration method, either grid method with the range or using empirical theta file (then the file name is given instead of the range [-4,4]). W(1) means using weighed sum in the integration approximation; W(0) means unweighed sum is used. T# is the number of theta used in integral approximation. TD# is the dimension of theta. I# is the total item number. M: is the model specification, P: is the parameteriza specification.

2.	From left to right: The mean sum of squares of residuals; the elements of M (rowwise), the elements of e.

3.	(***********) Not meaningful, used to seperate each round of calculation.

For each calculation, you have the options to either append the outcome to an existing file or write the outcome to a new file. And if you empty the output file frame in the data file source window, the outcome is presented in the program window only.


Getting Started

First, two item parameter files are needed to calaculate the linking coefficients. Then the initial parameter concerning the calculation needs to be set. This can be accomplished in two ways. The first one is to load a previously saved initial parameter file by choosing the menu item File|Load Linking Ini. The second is to compose a new initial parameter set by choosing the menu item File|New Linking Ini. For more information about the linking initial parameter dialog, see the linking dialog of this help file.

To run the linking program after choosing the correct initial parameter setting, click the Link button in the initial parameter dialog or the menu item Run|Linking.

Besides the linking, this program contains some editting functions like copy, paste, clear,  view and print file such that information can be exchanged with other Window programs.

Run Sample File

Choose menu File|Load Linking ini, pick the file Mdini.ini. Then click the "Link" button in the linking dialog window.


Integral Approximation

In the TCF and ICF methods, the differences are smoothed over the domain of theta by means of integral. There are two options in IPLINK to approximate the integrals.

1.	Grid method
In this method an k dimension (with k being the dimension of theta) is chosen as the region of integral approximation. The one-dimensional length of the grid is determined by the beginning and the ending parameters. The number of equally spaced grid points (theta points) is decided by the grid point parameter.

2.	Empirical theta method
Instead of using equally spaced grid points, users can also provide empirical (examinee) theta file as theta values to be used in the approximation.

In both methods, users have the option to use unweighed or weighed sum  when calculating the approximation. In the latter case, the standard normal density function (for given grid or empirical theta point) is used as the weight function.


Linking Dialog Window

This dialog is used to set linking initial parameter and make linking. The setting is divided into several groups:

General Setting

Data File Format

Intergration Parameters

Locate Data Files


Linking General
Linking Setting

General Setting

Results are always presented on screen even when there is no output file chosen. The Save As button at the bottom of the window saves the current linking initial setting in a new file. The OK button saves the current setting in current file name. The Link button execute the linking process.

Dimension. The dimention of the item parameter a or theta.

Linking Function Type. See the model selection section for more information about which function/model to choose.

Parameterization. See the parameterization and linking specification section for more information about the choices.

Data File Format

The settings in this section are to determine the input files (from, to, empirical) formats. From and To files (or, focus and reference group item parameter files) usually have the same format.

Pick File. choose which kind of file to set the format.

Type. Besides the user defined format, user can choose some predetermined formats.

Row and Column. See the input file format section for more information about specific row and column formats

Multiplied by. Determines the data is logistic or normal type.

Save Shown Format. After filling in the row and column formats for each kind of data file, user should click the Save Shown Format once to save the setting before moving to another kind of data file.

Integration Parameters

Grid point. number of grid points used in the Grid Point integral approximation. When Empirical method is used, the grid point should be zero.

Grid Range. The range used on each diemension

Weighed Sum. if checked, the standard normal density function will be used as weight function.

Locate Data Files

The From, To and Empirical buttons are used to located the data files. After files are chosen, click on the Add to list button to add. (Linking can be done on multiple pairs.) To delete a pair from the list, highline the pair on the list window, then click on the Delete from  List button. Similar procedure for Show Item.

Note: To add pairs using empirical theta set, first set the grid point to zero.


Main Menu and Toolbar

Since IPLINK is built on top of a notepad equivalent program, most menu items should be familiar to users. Here only the linking related menu items are described.

Menu

File|New Linking Ini. Open the linking initial parameter dialog to compose a new initial parameter file.

File|Load Linking Ini. Load existing linking initial parameter file and open the linking initial parameter dialog for editing and linking.

Run|Linking. Run linking using existing linking initial parameter file.

Run|Iterative Linking. Run iterative linking using existing existing linking initial parameter file.

Toolbars

(from left to right, in groups)

Open new text file; Open existing text file; Save text file

Cut; Copy; Paste; Print text file; Help(content)

Load existing linking initial file; Run linking with existing initial file


Model Selection

The model selections indicate which function to be minimized to find the linking parameters. The available options are

1.	Direct method
The sum of squares of the differences between the corresponding elements of a and a1, b and b1, d and d1, respectively. The minimization procedure is basically a mutlivaiate linear regression procedure.

2.	Reserved fro future use.

3.	TCF (Test Characteristic Function) method
The sum of squares of the diferences between the test scores of the same examinee in the two groups. The minimization method is a modified Newton method, with or without using the second-derivative.

4.	ICF (Item Characteristic Function) method
The sum of squares of the diferences between item probabilities for each item and each examinee. The minimization procedure is the same as in the TCF method.


Overview

IPLINK is a program to find the linking parameters for two given item parameter files (focus and reference groups). The objective is to minimize the criterion functions with respect to the linking parameters. IPLINK can handle various types of parameterization of the item characteristic function. There are currently three types of criterion functions to choose from in IPLINK: the direct method, the TCF method and the ICF method. For more details, see Model Selection.

This online help is organized in two sections: Usage and technical details.

Any question and/or comment are welcome to improve this program. The most frequent asked question seems to be about the setting of data file format, please e-mail a sample data file to the author if you have the problem.

For any comments or questions, please contact the authors at

Kevin Lee

gs01kkl@panther.gsu.edu

csglekv@mindspring.com


Parameterization

The item success probability function has the following general form:

P() = c + (1 - c)L[]

where L[] is either the logistic or normal distribtion function.

Using the conventional notations, we list the specifications of parameterizations and linking as follows. a(1), theta(1), and b(1) are the k dimension vectors with k being the ability dimension. d(1) is a scale number used in parameterization 2 and 4 below. The notation with and without the (1) represents item parameters from two different groups being linked. M (k X k dimension) and e (k X 1) are the linking parameters. Four kinds of parameterization and their corresponding linking methods are presented below.

Parameterization	Linking
1 L[a'(theta-b)]	theta1=M*theta+e, a1=inv{M}'a, b1=M*b+e
2 L[a'theta+d]	theta1=inv{M}theta+e, a1=M'a, d1=d-a'M*e
3 L[a'(theta-b)]	theta1=inv{M}theta+e, a1=M'a, b1=inv{M}b+e
4 L[a'theta+d]	theta1=M*theta+e, a1=inv{M}'a, d1=d-a'inv{M}e

For example, case #1 is assumed in a unidimensional linking program such as EQUATE although different notations are used there. For the output from a multidimensional IRT calibration program such as NORARM,  #2 or #4 are used. Other setups can be transferred to one of the above.

Important note: different parameterization yields different solutions.