Measuring Romance with Rasch: Batchelor Australia, 2018, (Series 10)

Batchelor Aus Girl Cumulative Measures
Winsteps Table 45 Plot: Cumulative girl measures after each episode

 

MEASURE TASK - MAP - Girl Oct 4
           EASY|LESS
  100          +  99 Max
               |
               |
               |
               |
   90          +
               |
               |
               |
               |
   80          +
            X  |
               |
               |
   70          +T
               |
               |
               |
               |
   60         T+
               |
               |
               |
               |
   50         S+
               |S 02 Brittany    03 Brooke
           XX  |
               |  02 Sophie
          XXX  |  04 Cass
   40    XXXX  +  05 Dasha
           XX M|  08 Jamie-Lee
            X  |  06 Emily       07 Shannon     08+1 Tenille   10+3 Romy
            X  |  09+3 Alisha
   30          +  09+1 Deanna
               |  11+3 Cat       13+3 Rhiannon
            X S|
           XX  |M
            X  |  09+2 Brittney  12+3 Ashlea    16 Aleksandra
   20          +  15 Blair
               |
               |  14 Vanessa     17 Steph
              T|  18 Cayla       19 Christina
               |
   10          +
               |
               |  20 Kayla
               |
               |S 21 Juliana     22 Renee
    0          +  98 Min
               |
               |
               |
  -10          +
               |
               |
               |
               |  23 Autumn      24 Suzie       25 Urszula
  -20          +
           HARD|MORE

The girls' desirabilities are shown in the Wright Person-Item map: Winsteps Table 16.3.


Girl Oct 4 STATISTICS:  MEASURE ORDER
------------------------------------------------------------------------------------------------
|ENTRY   TOTAL  TOTAL           MODEL|   INFIT  |  OUTFIT  |EXACT MATCH|        |              |
|NUMBER  SCORE  COUNT  MEASURE  S.E. |MNSQ  ZSTD|MNSQ  ZSTD| OBS%  EXP%|DISPLACE| Girl Oct 4   |
|------------------------------------+----------+----------+-----------+--------+--------------|
|    30      5      3   100.0A   19.7| .13   -.6| .11   -.6|100.0  90.2|      .0| 99 Max       |
|     3     34     16    47.8     3.0|1.18    .7|1.11    .4| 31.3  44.3|      .1| 03 Brooke    |
|     1     33     17    46.8     3.0| .67  -1.1| .74   -.4| 58.8  46.8|      .1| 02 Brittany  |
|     2     29     17    43.2     3.0|1.03    .2| .77   -.2| 47.1  53.8|      .1| 02 Sophie    |
|     4     27     15    41.9     3.1| .78   -.6| .84   -.1| 53.3  49.5|      .1| 04 Cass      |
|     5     23     14    38.8     3.5|1.03    .2|1.21    .5| 35.7  54.7|      .1| 05 Dasha     |
|     8      8      6    36.9     5.1| .79   -.2| .71   -.1| 66.7  51.9|      .1| 08 Jamie-Lee |
|     9     18     11    35.6     4.3| .88   -.1| .81    .1| 72.7  56.8|      .1| 08+1 Tenille |
|    13     15      9    35.1     5.2|1.07    .3| .87    .3| 55.6  61.7|      .1| 10+3 Romy    |
|     6     20     14    34.9     3.8| .93    .0| .75    .0| 57.1  56.0|      .1| 06 Emily     |
|     7     19     13    34.2     4.0| .52  -1.1| .58   -.2| 69.2  61.1|      .1| 07 Shannon   |
|    12     14      9    32.4     5.3| .58   -.7| .41   -.1| 66.7  64.3|      .0| 09+3 Alisha  |
|    10      4      4    30.1     6.7|1.17    .5| .84    .1| 50.0  52.8|      .1| 09+1 Deanna  |
|    14     13      9    29.5     5.4| .88    .0| .81    .3| 55.6  65.4|      .0| 11+3 Cat     |
|    16     12      8    28.6     6.1|1.94   1.3|1.63    .9| 62.5  70.5|      .0| 13+3 Rhiannon|
|    11      2      3    22.7     9.7| .18  -1.0| .19  -1.0|100.0  67.5|      .1| 09+2 Brittney|
|    19      7      5    21.6     8.2| .79    .0| .77    .3| 60.0  75.9|      .0| 16 Aleksandra|
|    15     10      8    21.4     5.8| .42  -1.1| .31   -.2| 75.0  65.2|      .0| 12+3 Ashlea  |
|    18      8      6    20.0     6.6|1.46    .9|1.39    .7| 66.7  67.8|      .0| 15 Blair     |
|    17      8      7    16.7     6.0|1.22    .6|1.66    .9| 42.9  59.3|      .0| 14 Vanessa   |
|    20      6      5    15.6     7.5| .64   -.5| .49    .0| 60.0  64.2|      .0| 17 Steph     |
|    21      5      4    13.5     8.1|1.21    .5| .83    .4| 50.0  64.9|      .0| 18 Cayla     |
|    22      5      4    13.5     8.1|1.21    .5| .83    .4| 50.0  64.9|      .0| 19 Christina |
|    23      4      4     6.7     8.6| .20   -.9| .14   -.5|100.0  78.0|      .0| 20 Kayla     |
|    24      3      3      .5     9.8| .61   -.3| .51    .1| 33.3  53.2|     -.1| 21 Juliana   |
|    25      3      3      .5     9.8| .61   -.3| .51    .1| 33.3  53.2|     -.1| 22 Renee     |
|    29      0      2      .0A   19.3|3.71   2.0|9.02   2.8| 50.0  81.3|   -56.1| 98 Min       |
|    26      1      2   -17.4    13.8| .23   -.3| .25   -.4|100.0  79.0|     -.1| 23 Autumn    |
|    27      1      2   -17.4    13.8| .23   -.3| .25   -.4|100.0  79.0|     -.1| 24 Suzie     |
|    28      1      2   -17.4    13.8| .23   -.3| .25   -.4|100.0  79.0|     -.1| 25 Urszula   |
|------------------------------------+----------+----------+-----------+--------+--------------|
| MEAN    11.3    7.5    23.9     7.7| .88   -.1| .99    .1| 63.4  63.7|    -1.9|              |
| P.SD     9.8    4.9    23.1     4.4| .67    .7|1.54    .7| 21.3  11.3|    10.1|              |
------------------------------------------------------------------------------------------------

The Batchelor Australia is a TV series on Australian TV, Network 10, tenplay.com.au. Series 6 started on August 15, 2018.

Each girl (contestant) is a row in the data matrix. Each episode, or part of an episode, is a column (item, task) in the data matrix. In the first episode, 25 girls met batchelor Nick Cummins. 3 girls were eliminated. 1 girl, Brooke, was awarded the "key to the batch pad" for a private meeting with Nick.

In most episodes, the eliminated girls are score 0. Other girls are scored in higher categories depending on the attention they received from Nick. Since the scoring varies across episodes, the Partial Credit Model, ISGROUPS=0, is used. For details of each episode, please see Wikipedia: The Batchelor Australia (series 6).

The girls are listed by name. The number immediately preceding each name is their order of elimination, counting backwards. There are two additional rows. These are used for hypothetical "Minimum" (who is less desirable than anyone) and "Maximum" (who is more desirable than anyone). These are anchored at 0 and 100 to establish a constant frame-of-reference across the Batchelor episodes.

The columns (items) are labeled with codes such as "1-Meet". "1" indicates the week number. "Meet" indicates the type of event. In addition to a column for each episode, there are three additional columns. The first data column, "Pre", is a Bayesian item containing ratings for the contestants (all the same), Maximum and Minimum. This gives us reasonable estimates to launch the process. The last item column, "Now", is also Bayesian. This gives the current best estimate for each active girl in the anchored-frame of reference. It is similar to "Pre", but inactive contestants are omitted. This column models the fact that contestants are changing their desirability. Nick is liking some more, and others less. The very last column, "Wins", is weighted zero, so that it does not influence any of the contestant estimates. This is used to estimate the probability for each contestant based on the current difficulty of winning the competition. This difficulty is such that the sum of the probabilities for the active contestants of succeeding on this "item" is 1.0. The probabilities are reported in the XFILE= as (RESIDUAL or 1-RESIDUAL) for this item. This is the Winning Probability Percent in the Table above.

After each episode, the outcomes are scored based on the Nick's opinions and actions, and entered into an Excel spreadsheet, available here. This is then converted into the Winsteps control and data file shown below and here by means of the Winsteps Excel/RSSST menu. USCALE=10 and other control instructions have been added to rescale the measures into more friendly numbers.


&INST
Title= "batchelor-aus-2018.xls"
; Excel file created or last modified: 10/4/2018 9:26:55 PM
; Sheet1
;     Excel Cases processed = 30
; Excel Variables processed = 24
ITEM1 = 1 ; Starting column of item responses
NI = 18 ; Number of items
NAME1 = 20 ; Starting column for person label in data record
NAMLEN = 14 ; Length of person label
XWIDE = 1 ; Matches the widest data value observed

ISGROUPS = 0 ; Partial Credit model: in case items have different rating scales
IWEIGHT = 5W4 ; for "Win"
USCALE = 10 ; high score = high ability, rescaled for 0-100 = 10 logits
UDECIMALS = 1
PAFILE=*
29 0    ; anchor minimum performance at 0
30 100  ; anchor maximum performance at 100
*
CONVERGE=B
LCONV=.01
RCONV=.1
FREQ = HARD ; for the Wright Person-Item Map
LESS = MORE
MORE = LESS
RARE = EASY
TITLE = Batchelor Australia 2018 - October 4
PERSON = Girl Oct 4
ITEM = TASK
LINELENGTH = 120
TFILE=*
16.3
17.1
*

CODES = "01234 " ; matches the data
TOTALSCORE = Yes ; Include extreme responses in reported scores
; Person Label variables: columns in label: columns in line
@Name = 1E13 ; $C20W13
&END ; Item labels follow: columns in label
0-Pre ; Item 1 : 1-1
1-Meet ; Item 2 : 2-2
2-Heli ; Item 3 : 3-3
3-Golf ; Item 4 : 4-4
4-Arrows ; Item 5 : 5-5
5-Family ; Item 6 : 6-6
6-Campout ; Item 7 : 7-7
7-Pre ; Item 8 : 8-8
7-Bounce ; Item 9 : 9-9
8-Toga ; Item 10 : 10-10
9-Lies ; Item 11 : 11-11
10-Cars ; Item 12 : 12-12
11-Obs ; Item 13 : 13-13
12-SWAY ; Item 14 : 14-14
13-Bowls ; Item 15 : 15-15
14-Home ; Item 16 : 16-16
15-Dates ; Item 17 : 17-17
Finale ; Item 18 : 18-18
END NAMES
1313132 2242113310 02 Brittany
1322131 1123114210 02 Sophie
1433141 243213110  03 Brooke
1323112 22313120   04 Cass
1313321 1212210    05 Dasha
1212121 2311120    06 Emily
1332122 111110     07 Shannon
       121310      08 Jamie-Lee
1222121 3220       08+1 Tenille
       1120        09+1 Deanna
       110         09+2 Brittney
1222122 20         09+3 Alisha
1232222 10         10+3 Romy
1222211 20         11+3 Cat
1212121 0          12+3 Ashlea
1212123 0          13+3 Rhiannon
1121120            14 Vanessa
121220             15 Blair
12220              16 Aleksandra
12120              17 Steph
1220               18 Cayla
1220               19 Christina
1210               20 Kayla
120                21 Juliana
120                22 Renee
10                 23 Autumn
10                 24 Suzie
10                 25 Urszula
0      0           98 Min
2      2         1 99 Max

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