Measuring Romance with Rasch: Batchelor Australia, 2019, (Series 7)

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

 

MEASURE EPISODE - MAP - Girl Sept 20
            HARD|MORE
      XXXXXXXX S|  Abbie      Chelsie    Helena
   60  XXXXXXX M+  Elly       Emma       Kristen    Mary       Monique    Sogand
            XX  |  Julia      Nichole    Nikki      Vakoo
             X S|  Brianna    Cassandra  Georgie    Hannah     Isabelle   Jessica    Rachael    Renee
               T|  Jessie
                |M Tash
                |
   50        X  +
                |
                |
                |
                |
                |S
   40           +
                |
                |
                |
                |  Danush     Sam        Tara
                |
   30           +T
                |
                |
                |
                |
                |  Keely      Sophie
   20           +
            EASY|LESS

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


Girl Sept 20 STATISTICS:  MEASURE ORDER
--------------------------------------------------------------------------------------
|ENTRY   TOTAL  TOTAL           MODEL|   INFIT  |  OUTFIT  |EXACT MATCH|             |
|NUMBER  SCORE  COUNT  MEASURE  S.E. |MNSQ  ZSTD|MNSQ  ZSTD| OBS%  EXP%| Girl Sept 20|
|------------------------------------+----------+----------+-----------+-------------|
|     1     60     19    62.5     1.1| .88  -.08| .71  -.63| 31.6  21.9| Chelsie     |
Eliminated:
|     3     64     18    62.0     1.0| .81  -.29| .97   .08| 11.1  19.6| Helena      |
|     2     77     19    60.9      .9|2.36  2.56|1.41  1.06| 10.5  20.7| Abbie       |
|     5     74     16    60.7      .9|1.48  1.16|1.29   .74| 18.8  17.6| Elly        |
|     4     88     17    59.9      .8| .77  -.58| .74  -.51| 11.8  17.7| Emma        |
|    15     42      6    59.7     1.0|1.86  1.53|1.70   .89| 16.7  22.6| Monique     |
|     6     79     13    59.7      .8| .98   .08| .91   .02| 15.4  16.5| Kristen     |
|     8     73     11    59.5      .8| .37 -2.10| .37 -1.10| 18.2  16.5| Mary        |
|     7     79     12    59.4      .8|1.14   .49| .83  -.11| 16.7  16.5| Sogand      |
|    14     56      7    59.2      .9|1.22   .62|1.05   .38| 28.6  20.4| Vakoo       |
|     9     81     11    59.0      .8| .84  -.32| .67  -.36|  9.1  16.7| Nichole     |
|    10     68      9    58.9      .9| .65  -.84| .69  -.18| 11.1  18.1| Nikki       |
|    16     45      5    58.5     1.1|1.17   .47| .90   .38| 40.0  25.4| Julia       |
|    22     28      3    57.4     1.6|1.95  1.14|1.34   .69| 33.3  37.8| Georgie     |
|    20     30      3    57.4     1.5|1.04   .34| .71   .24| 33.3  37.5| Renee       |
|    23     29      3    57.2     1.6|1.70   .94|1.17   .58| 33.3  38.0| Hannah      |
|    18     32      3    56.9     1.7| .82   .16| .57   .10| 33.3  37.8| Jessica     |
|    13     87      8    56.6     1.1| .60  -.53| .84   .16| 25.0  25.3| Brianna     |
|    17     59      5    56.6     1.3| .84   .04| .77   .29| 20.0  26.7| Isabelle    |
|    11    106     10    56.5     1.1| .69  -.41| .57  -.32| 30.0  23.1| Rachael     |
|    12    101      9    56.0     1.2| .73  -.23| .63  -.14| 22.2  24.7| Cassandra   |
|    19     52      4    54.7     2.1| .28  -.49| .22  -.37| 50.0  32.9| Jessie      |
|    26     38      3    52.8     3.4| .30  -.24| .20  -.40| 33.3  42.4| Tash        |
|    21     23      2    33.8    33.9| .03  -.96| .03  -.96|100.0  96.2| Danush      |
|    24     23      2    33.8    33.9| .03  -.96| .03  -.96|100.0  96.2| Sam         |
|    25     23      2    33.8    33.9| .03  -.96| .03  -.96|100.0  96.2| Tara        |
|    27     21      2    21.9    21.1| .13  -.58| .13  -.57|100.0  88.2| Keely       |
|    28     21      2    21.9    21.1| .13  -.58| .13  -.57|100.0  88.2| Sophie      |
|------------------------------------+----------+----------+-----------+-------------|
| MEAN    55.7    8.0    53.1     6.2| .85    .0| .70   -.1| 37.6  37.2|             |
| P.SD    25.8    5.7    11.7    10.9| .60    .9| .44    .6| 30.7  27.1|             |
--------------------------------------------------------------------------------------

The Batchelor Australia is a TV series on Australian TV, Network 10, tenplay.com.au. Series 7 started on July 31, 2019 and ended on Sept. 20, 2019.

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, 20 girls met batchelor Matt Agnew. 2 girls were eliminated. 1 girl, Elly, was awarded the "Golden Ticket" for a trip to Melbourne with Matt.

At the end of each episode, there is a Rose Ceremony.The girls are scored by the order in which they receive roses. The lowest ranked are eliminated from future episodes. Since the number of girls varies across episodes, the Partial Credit Model, ISGROUPS=0, is used. For details of each episode, please see Wikipedia: The Batchelor Australia (series 7).

The girls are listed by name in the Excel spreadsheet. 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 "Ep. 1". "1" indicates the episode number. 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. Matt 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 EXPECTATION for this item. This is the Winning Probability Percent in the Table above.

After each episode, the outcomes are scored based on the Matt's assignment of roses and other 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-2019.xls"
; Excel file created or last modified: 9/20/2019 2:21:30 PM
; Sheet1
;     Excel Cases processed = 30
; Excel Variables processed = 19
ITEM1 = 1 ; Starting column of item responses
NI = 18 ; Number of items
NAME1 = 38 ; Starting column for person label in data record
NAMLEN = 10 ; Length of person label
XWIDE = 2 ; Matches the widest data value observed

; extra control variables
ISGROUPS = 0 ; Partial Credit model: Episodes have different rankings
STKEEP=No ; when girls drop out, drop out their ratings
IWEIGHT = 6W4 ; for "Win" and team events
USCALE = -10 ; low score = high desirability, rescaled for 0-100 = 10 logits
UDECIMALS = 1
PAFILE=*
30 0    ; anchor minimum performance at 0
29 100  ; anchor maximum performance at 100
*
CONVERGE=B
LCONV=.005
RCONV=.05
FREQ = HARD ; for the Wright Person-Item Map
LESS = MORE
MORE = LESS
RARE = EASY
TITLE = Batchelor Aus 2019 Sept 20
PERSON = Girl Sept 20
ITEM = EPISODE
LINELENGTH = 120
PSELECT={A-Z}  ; only analyze active ladies
STKEEP=NO ; drop out eliminated rankings
TFILE=*
; IDELETE=+1
PDELETE=29-30
MAXPAG=60
16.3
IDELETE=
MAXPAG=100
17.1
*

CODES = "  . 0 1 101112131415161718192 3 4 5 6 7 8 9 " ; matches the data
CODERANGE = 20 - 21
TOTALSCORE = Yes ; Include extreme responses in reported scores
; Person Label variables: columns in label: columns in line
@Girls = 1E9 ; $C38W9
&END ; Item labels follow: columns in label
Pre ; Item 1 : 1-2
Ep. 1 ; Item 2 : 3-4
Ep. 2 ; Item 3 : 5-6
Ep. 3 ; Item 4 : 7-8
Ep. 4 ; Item 5 : 9-10
Ep. 5 ; Item 6 : 11-12
Ep. 6 ; Item 7 : 13-14
Ep. 7 ; Item 8 : 15-16
Ep. 8 ; Item 9 : 17-18
Ep. 9 ; Item 10 : 19-20
Ep.10 ; Item 11 : 21-22
Ep.11 ; Item 12 : 23-24
Ep.12 ; Item 13 : 25-26
Ep. 13 ; Item 14 : 27-28
Ep.14 ; Item 15 : 29-30
Ep.15 ; Item 16 : 31-32
Ep.16 ; Item 17 : 33-34
Wins 0 ; Item 18 : 35-36
END NAMES
2 2 2 4 8 2 1 2 6 9 2 5 2 3 1 2 1 1  Chelsie
2 9 205 1 1 5 3 103 1 3 5 2 2 1 0    Abbie
2 106 7 5 3 3 2 3 5 7 1 1 1 3 3      Helena
2 1113103 8 2 1 8 4 5 2 3 4 4        Emma
2 1 8 1 156 9 2 1 1 3 6 4 5          Elly
2 8 156 114 132 2 2 4 4 6            Kristen
2 3 1 15127 124 4 6 6 7              Sogand
2 7 11126 5 4 4 7 7 8                Mary
2 129 2 7 146 4 9 8 8                Nichole
2 . 7 114 13115 5 10                 Nikki
2 18141413118 4 1111                 Rachael
2 1718179 12104 12                   Cassandra
2 16161614107 6                      Brianna
2 4 3 8 169 14                       Vakoo
2 . 5 3 2 1515                       Monique
2 . 4 131016                         Julia
2 14179 17                           Isabelle
2 . 1218                             Jessica
2 131918                             Jessie
2 . 1018                             Renee
2 . 21                               Danush
2 5 21                               Georgie
2 6 21                               Hannah
2 . 21                               Sam
2 . 21                               Tara
2 1521                               Tash
2 19                                 Keely
2 19                                 Sophie
1 .                                  Best
3 .                                  Worst

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