• Data
• BILOG-MG (1PL-F.BLM)
• PARSCALE (1PL-F.PSL)
• MULTILOG (1PL-F.MLG)
• Comparison of keywords used

Getting started - fitting a 1-parameter model to frequency data

The data used are in the form of a frequency table stored in the file lsat6.frq. There are 32 patterns containing responses to 5 items, as shown below. A frequency of 0 was obtained for pattern 11, and thus analyses are based on 31 groups. The first 3 fields contain the pattern identification. This is followed in column 5 by the pattern responses. The frequencies for each pattern, which are used as weights in the syntax to follow, are given in columns 10-13.

  1 00000   3
  2 00001   6
  3 00010   2
  4 00011  11
  5 00100   1
  6 00101   1
  7 00110   3
  8 00111   4
  9 01000   1
 10 01001   8
 11 01010   0
 12 01011  16
 13 01100   0
 14 01101   3
 15 01110   2
 16 01111  15
 17 10000  10
 18 10001  29
 19 10010  14
 20 10011  81
 21 10100   3
 22 10101  28
 23 10110  15
 24 10111  80
 25 11000  16
 26 11001  56
 27 11010  21
 28 11011 173
 29 11100  11
 30 11101  61
 31 11110  28
 32 11111 298

Equivalent syntax files for a 1-parameter model in BILOG-MG, MULTILOG and PARSCALE are given in the next three sections. In some cases, similar keywords are set to different values for the programs. This is done to obtain equivalent output, as the iterative procedures used in these programs differ. For example, the number of EM cycles is set to 50 for BILOG-MG, but to 200 for PARSCALE. A maximum of 100 MML cycles is specified in the case of MULTILOG.

Note that the format specification differs between the programs due to variations in the prescribed order of data elements. BILOG-MG and PARSCALE expect the ID field first, followed by the frequency (weight) and the response pattern:

(3A1,T10,F4.0,T5,5A1)

In MULTILOG, the response pattern is read after the ID field and the frequency is read last:

(3A1,T5,5A1,T10,F4.0)

In both cases, the "T" operator is used to move to specific fields in the data file.

MULTILOG also requires explicit information about the data characteristics at the end of the syntax file, before the variable format statement. In this example where a one-parameter model is used, the specifications are the number of response codes (2), the actual codes (01), the vector of correct responses for the five items (11111) and whether there are missing data present (N). This information precedes the actual format statement.

The other two programs assumes, by default, 0,1 responses where 0 indicates an incorrect and 1 a correct response to an item.

PARSCALE does not explicitly implment the one-parameter logistic model. However, when items are similar (as in this example: all five items are 0,1 scored items), they can be grouped in one block and the estimation of a common slope (CSLOPE) within that block can be requested. Generally, this common slope will then not turn out to be equal to one, as in the 1PL or Rasch model, but the results will be comparable.

While BILOG-MG and PARSCALE performs calibration and scoring in different phases of the same run, MULTILOG requires separate calibration and scoring runs. This is specified using either the RA (for calibration) or SC (for scoring) option on the PROGRAM command.

In the last section, an overview is provided of similarities and differences in keyword specifications for the three programs.

BILOG-MG (1PL-F.BLM)

The syntax file 1pl-f.blm shown below can be found in the compare subfolder of the BILOG-MG installation.

ITEM PARAMETERS ESTIMATION WITH 1PL MODEL USING BILOG-MG 1
     USING FREQUENCY DATA: RESPONSE PATTERNS PLUS WEIGHTS
>COMMENT ;
>GLOBAL DFNAME='..\LSAT6.FRQ',NPARM=1,NWGHT=3,SAVE;
>SAVE PARM='1PL-F.PAR';
>LENGTH NITEMS=5;
>INPUT NTOTAL=5,NFMT=1,TYPE=2,SAMPLE=1000,NIDCHAR=3;
>ITEM INUMBERS=(1(1)5);
>TEST TNAME=TESTIT,INUMBER=(1(1)5);
(3A1,T10,F4.0,T5,5A1)
>CALIB NQPT=30,CYCLES=50,CRIT=0.001,NEWTON=0;

PARSCALE (1PL-F.PSL)

The syntax file 1pl-f.psl shown below can be found in the compare subfolder of the PARSCALE installation.

ITEM PARAMETERS ESTIMATION WITH 1PL MODEL USING PARSCALE 4.1
     USING FREQUENCY DATA: RESPONSE PATTERNS PLUS WEIGHTS
>COMMENT
       NOTE THAT "CSLOPE" IS USED TO FIT AN EQUIVALENT RASCH MODEL
       PRIORS DO NOT WORK IN THIS VERSION, SO THE COMMON SLOPE CANNOT
       FORCED TO BE 1

>FILES DFNAME='..\LSAT6.FRQ',SAVE;
>SAVE  PAR='1PL-F.PAR';
>INPUT NTOTAL=5,LENGTH=5,NFMT=1,WEIGHT,MAXCAT=2,SAMPLE=1000,NIDCHAR=3;
(3A1,T10,F4.0,T5,5A1)
>TEST  TNAME=TESTIT,ITEMS=(1(1)5),NBLOCK=1;
>BLOCK BNAME=ONE,NITEMS=5,NCAT=2,ORIGINAL=(0,1),CSLOPE;
>CALIB GRADED,NQPT=30,CYCLES=200,CRIT=0.001,NEWTON=0;

MULTILOG (1PL-F.MLG)

The syntax file 1pl-f.mlg shown below can be found in the compare subfolder of the MULTILOG installation.

ITEM PARAMETERS ESTIMATION WITH 1PL MODEL USING MULTILOG 7
     USING FREQUENCY DATA: RESPONSE PATTERNS PLUS WEIGHTS
>PROBLEM  RANDOM,PATTTERN,NITEMS=5,NPATTERN=32,NGROUP=1,NCAT=3,DATA='..\LSAT6.FRQ';
>TEST     ALL L1 NC=(2(0)5),HI=(1(0)5);
>ESTIMATE NCYCLES=100, ITERATIONS=4, CCRIT=0.001;
>SAVE     ;
>END;
2
01
11111
N
(3A1,T5,5A1,T10,F4.0)

Comparison of keywords used

In the table below, the information specified in the three syntax files is compared in terms of the keywords used to specify each piece of information. Assumptions in terms of the nature of responses in BILOG-MG and PARSCALE are not shown, and similarly the additional information on responses required in MULTILOG syntax is not included.

Table: Syntax specification of a 1PL model for frequency data