Measuring the Cooks with Rasch: Masterchef Australia, 2018, (Series 10)

Masterchef 2018 Cook Cumulative Measures
Winsteps Table 45 Plot: Cumulative person measures after each cooking task

 

MEASURE      TASK - MAP - COOK July 31
                 HARD|MORE
  100                +  Maximum at 100
                     |
                     |
                     |
                     |
   90                +
                     |
                     |
                     |
                     |
                     |
   80                +
                     |
                     |
                     |T
                     |
                     |
   70                +
                     |
                     |
                     |
                  #  |
   60             # T+
                 .#  |S
                     |
                 .# S|  Guest Chef
             .#####  |
            #######  |  1 Sashi Cheliah        3 Khanh Ong
   50        .#####  +  6 Reece Hignell        8 Kristen Sheffield
             .##### M|  10 Sarah Clare         12* Gina Ottaway       18 Loki Madireddi (i)  9 Brendan Pang (16)
            #######  |  2 Ben Borsht           5 Chloe Carroll        7 Samira Damirova
                ###  |M 12 Aldo Ortado         13 Lisa Diep           15 Genene Dwyer        4 Jess Liemantara
                 .# S|  11 Hoda Kobeissi
   40            ##  +  17 Jo Kendray
                ###  |
                  #  |  14 Jenny Lam           20 Tim Talam
                    T|  22 Denise Valdez
                     |  19 Michelle Walsh
                     |  21 Adele Elliott       23 Metter Chin
   30                +
                     |S
                     |  24 Brett McGrath
                  .  |
                     |
                     |
   20                +
                     |
                     |
                     |T
                     |
   10                +
                     |
                     |
                     |
                     |
                     |
    0                +  Minimum at 0
                 EASY|LESS

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


         COOK July 31 STATISTICS:  MEASURE ORDER
--------------------------------------------------------------------------------------------------------
|ENTRY   TOTAL  TOTAL           MODEL|   INFIT  |  OUTFIT  |EXACT MATCH|        |                      |
|NUMBER  SCORE  COUNT  MEASURE  S.E. |MNSQ  ZSTD|MNSQ  ZSTD| OBS%  EXP%|DISPLACE| COOK July 31         |
|------------------------------------+----------+----------+-----------+--------+----------------------|
|    27    3.0    3.0   100.0A   18.8| .11   -.6| .11   -.6|100.0  90.3|      .0| Maximum at 100       |
|    25   19.0   12.0    55.4     6.1|1.19    .8|1.26    .8| 50.0  63.2|      .1| Guest Chef           |
|     3   83.3   43.0    51.6     2.1|1.13    .7| .99    .0| 37.5  49.3|      .0| 3 Khanh Ong          |
|     1   88.9   45.5    50.9     2.0| .94   -.3| .97   -.1| 48.7  49.2|      .0| 1 Sashi Cheliah      |<- Winner
|     6   68.4   33.0    50.1     2.4| .75  -1.1| .82   -.6| 60.5  53.4|      .0| 6 Reece Hignell      |
|     8   63.8   28.5    50.0     2.3|1.24   1.0|1.13    .5| 48.4  52.1|      .0| 8 Kristen Sheffield  |
|    12   48.1   21.0    48.6     3.0| .94    .0|1.09    .4| 53.0  55.1|      .0| 12* Gina Ottaway     |
|    18   31.4   13.3    48.1     3.9|1.50   1.1| .98    .1| 46.5  59.5|      .0| 18 Loki Madireddi (i)|
|    10   63.9   26.9    47.5     2.5|1.01    .1| .90   -.2| 58.4  54.5|      .0| 10 Sarah Clare       |
|     9   52.4   22.7    47.2     2.7|1.16    .6| .84   -.3| 49.5  54.3|      .0| 9 Brendan Pang (16)  |
|     2  101.3   45.0    46.8     2.0| .89   -.4|1.09    .5| 46.9  51.7|      .0| 2 Ben Borsht         |
|     7   88.7   36.5    45.4     2.1| .76   -.9|1.01    .1| 52.6  52.5|      .0| 7 Samira Damirova    |
|     5   95.3   41.5    45.3     2.1| .81   -.8| .84   -.6| 55.5  51.6|      .0| 5 Chloe Carroll      |
|    14   52.7   20.3    44.6     3.1| .98    .1| .89   -.1| 52.9  62.8|      .0| 13 Lisa Diep         |
|     4  110.8   47.5    44.3     2.0|1.33   1.5|1.17    .8| 53.4  54.4|      .0| 4 Jess Liemantara    |
|    16   45.6   18.2    43.9     3.3|1.49   1.1|1.52   1.1| 57.4  62.2|      .0| 15 Genene Dwyer      |<- most inconsistent
|    13   59.6   22.5    43.6     2.9| .74   -.6| .73   -.5| 67.3  63.0|      .0| 12 Aldo Ortado       |
|    11   64.3   25.2    43.0     2.8|1.04    .2| .77   -.5| 64.3  61.8|      .0| 11 Hoda Kobeissi     |
|    17   39.3   14.6    41.2     3.8|1.49   1.0| .81   -.1| 77.0  67.6|      .0| 17 Jo Kendray        |
|    15   57.2   21.3    37.8     3.4| .62   -.9| .57   -.8| 67.3  66.5|      .0| 14 Jenny Lam         |<- most consistent
|    20   35.4   12.2    36.8     4.0| .71   -.5| .56   -.5| 67.2  64.2|      .0| 20 Tim Talam         |
|    22   19.2    7.1    36.2     5.2|1.14    .4|1.72   1.0| 43.6  57.3|     -.1| 22 Denise Valdez     |
|    19   35.2   12.2    32.9     4.4|1.10    .4|1.01    .3| 65.6  57.3|      .0| 19 Michelle Walsh    |
|    21   30.2   10.1    32.8     4.4| .59  -1.0| .50   -.4| 40.5  50.4|     -.1| 21 Adele Elliott     |
|    23   20.0    7.0    32.4     5.0| .93    .0| .66   -.1| 42.9  45.9|     -.1| 23 Metter Chin       |
|    24   16.0    5.0    27.0     6.1| .44   -.9| .49   -.5| 80.0  60.0|     -.1| 24 Brett McGrath     |
|    26   10.0    3.0      .0A   15.2| .55   -.4| .36   -.3|100.0  77.7|   -13.2| Minimum at 0         |
|------------------------------------+----------+----------+-----------+--------+----------------------|
| MEAN    52.0   22.1    43.8     4.4| .95    .0| .88    .0| 58.8  58.8|     -.5|                      |
| P.SD    28.9   13.6    15.3     3.8| .33    .8| .33    .5| 15.6   9.2|     2.5|                      |
--------------------------------------------------------------------------------------------------------

Masterchef Australia is a TV series on Australian TV, Network 10, tenplay.com.au. Series 10 started on May 7th, 2018. An analysis of Masterchef Australia 2017 is here.

Each cook is a row in the data matrix. Each episode, or part of an episode, is a column (item, task) in the data matrix. The first two episodes are for qualification and are summarized in the "1-AU" column, the first "cooking" column (item, task) in the data matrix. In the first episode, 18 home-cooks cooked dishes good enough for immediate qualification, scored "1" here. In the second episode 6 more are added, scored "2".

In most subsequent episodes, the winner or winning group of cooks are scored "1", the losers are scored "3", and the middle group are scored "2". The judges often make finer gradations in their comments on the dishes, and these are shown by additional scored levels. Since the scoring varies across episodes, the Partial Credit Model, ISGROUPS=0, is used. For details of each episode, please see Wikipedia: MasterChef Australia (series 10).

The columns (items) are labeled with codes such as "2-IT". "2" indicates the week number. "IT" indicates the type of competition. They are Pre = Prior, AU=Auditions, IT=Free cook, MB=Mystery Box, PT=Pressure Test, elimination based on individual performance, IT=Invention Test, cooking for oneself, IQ=Immunity Qualifier, IC=Immunity Challenge, TC=Team Challenge, TE=Elimination based on Team performance, 2C=Second Chance, Now = best estimate of current ability, Wins=Probability of winning. "i" indicates the cook used an Immunity pin to bypass a Pressure Test. "-" indicates the cook is given a Bye for this event.

At the end of "Pressure Test" episodes, the losing cook is eliminated from the competition. In "Team Challenge" episodes, the contestants are divided into two or more teams with winning and losing teams. In team events (TC, 5-IT), the event is weighted inversely by the number of members of each team. In "Immunity" episodes, the winning cook competes against a professional Guest Chef. If the cook wins, the cook is awarded an "Immunity" pin (i), which can be used to escape from a future "Elimination" episode. Loki did this in 3-IC. He was later eliminated after choosing not to use the pin. Reece and Sashi also won pins. The Guest Chefs differ for each challenge, but are conceptualized to have the same ability and so are identified as a 25th contestant in the data matrix.

The cooks are listed by name. The number immediately preceding each name is their order of elimination, counting backwards. Brett was the first cook eliminated and so is numbered 24. The overall winner will be numbered 1. In addition to a row for each of the 24 contestants and one for the Guest Chefs, there are two additional rows. These are used for hypothetical "Minimum" (who is worse than anyone) and "Maximum" (who is better than anyone) chefs. These are anchored at 0 and 100 to establish a constant frame-of-reference across the Masterchef episodes.

In addition to a column for each cooking task, there are three additional columns. The first data column, "Pre", is a Bayesian item containing ratings for the contestants (all the same), the Guest Chef, 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 cook 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 abilities. Some are gaining skills from the experience. Others are wearying of it and want to leave. 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 cooks' performances are scored based on the judges opinions 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 reverse and rescale the measures, because lower score indicates higher ability.


&INST
Title= "Masterchef-2018.xls"
; Excel file created or last modified: 7/31/2018 10:04:01 PM
; Sheet1
;     Excel Cases processed = 27
; Excel Variables processed = 103
ITEM1 = 1 ; Starting column of item responses
NI = 97 ; Number of items
NAME1 = 99 ; Starting column for person label in data record
NAMLEN = 22 ; Length of person label
XWIDE = 1 ; Matches the widest data value observed

; extra control variables
ISGROUPS = 0 ; Partial Credit model: in case items have different rating scales
IWEIGHT = 6W4 ; for "Win" and team events
USCALE = -10 ; low score = high ability, rescaled for 0-100 = 10 logits
UDECIMALS = 1
PAFILE=*
26 0    ; anchor minimum performance at 0
27 100  ; 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 = Masterchef 2018 July 31
PERSON = COOK July 31
ITEM = TASK
LINELENGTH = 120
TFILE=*
16.3
17.1
*

CODES = "123456 -is" ; matches the data
TOTALSCORE = Yes ; Include extreme responses in reported scores
; Person Label variables: columns in label: columns in line
@Contestant = 1E21 ; $C99W21
&END ; Item labels follow: columns in label
0Pre ; Item 1 : 1-1
1-AU ; Item 2 : 2-2
1-IT ; Item 3 : 3-3
1-PT ; Item 4 : 4-4
2-MB ; Item 5 : 5-5
2-IT ; Item 6 : 6-6
2-PT ; Item 7 : 7-7
2-IQ ; Item 8 : 8-8
2-IC ; Item 9 : 9-9
2-TC 1/11 ; Item 10 : 10-10
2-TE ; Item 11 : 11-11
3-MB ; Item 12 : 12-12
3-IT ; Item 13 : 13-13
3-PT ; Item 14 : 14-14
3-IQ ; Item 15 : 15-15
3-IC ; Item 16 : 16-16
3-TC 1/10 ; Item 17 : 17-17
3TE1 ; Item 18 : 18-18
3TE2 ; Item 19 : 19-19
4-MB ; Item 20 : 20-20
4-IT ; Item 21 : 21-21
4-PT ; Item 22 : 22-22
4IC1 ; Item 23 : 23-23
4IC2 ; Item 24 : 24-24
4IC3 ; Item 25 : 25-25
4-TC 1/9 ; Item 26 : 26-26
4-TE ; Item 27 : 27-27
5-MB ; Item 28 : 28-28
5-IT 1/4 ; Item 29 : 29-29
5-PT ; Item 30 : 30-30
5-IQ ; Item 31 : 31-31
5-IC ; Item 32 : 32-32
5-TC 1/8 ; Item 33 : 33-33
5TE1 ; Item 34 : 34-34
5TE2 ; Item 35 : 35-35
6-MB ; Item 36 : 36-36
6-IT 1/2 ; Item 37 : 37-37
6-PT ; Item 38 : 38-38
6-IE ; Item 39 : 39-39
6-IC ; Item 40 : 40-40
6-TC 1/7 ; Item 41 : 41-41
6TE1 ; Item 42 : 42-42
6TE2 ; Item 43 : 43-43
6TE3 ; Item 44 : 44-44
7-MB ; Item 45 : 45-45
7-IT ; Item 46 : 46-46
7-PT ; Item 47 : 47-47
7IE1 ; Item 48 : 48-48
7IE2 ; Item 49 : 49-49
7IE3 ; Item 50 : 50-50
7-IC ; Item 51 : 51-51
7-TC 1/6 ; Item 52 : 52-52
7-TE ; Item 53 : 53-53
7-2C ; Item 54 : 54-54
8-MB ; Item 55 : 55-55
8-IT 1/2 ; Item 56 : 56-56
8-PT ; Item 57 : 57-57
8-IE ; Item 58 : 58-58
8-IC ; Item 59 : 59-59
8-TC 2/11 ; Item 60 : 60-60
8-TE ; Item 61 : 61-61
9-MB ; Item 62 : 62-62
9-IT ; Item 63 : 63-63
9-PT ; Item 64 : 64-64
9-IE ; Item 65 : 65-65
9-IC ; Item 66 : 66-66
9-TC 1/3 ; Item 67 : 67-67
9-TE ; Item 68 : 68-68
10MB ; Item 69 : 69-69
10IT ; Item 70 : 70-70
10P1 ; Item 71 : 71-71
10P2 ; Item 72 : 72-72
10P3 ; Item 73 : 73-73
10S1 ; Item 74 : 74-74
10S2 ; Item 75 : 75-75
10PT ; Item 76 : 76-76
11MB ; Item 77 : 77-77
11IT ; Item 78 : 78-78
11PT ; Item 79 : 79-79
11IE ; Item 80 : 80-80
11IC ; Item 81 : 81-81
11DE ; Item 82 : 82-82
11R1 ; Item 83 : 83-83
11R2 ; Item 84 : 84-84
11R3 ; Item 85 : 85-85
12MB ; Item 86 : 86-86
12IT ; Item 87 : 87-87
12PT ; Item 88 : 88-88
12P1 ; Item 89 : 89-89
12P2 ; Item 90 : 90-90
12P3 ; Item 91 : 91-91
12RC ; Item 92 : 92-92
13QF ; Item 93 : 93-93
13SF ; Item 94 : 94-94
13FS ; Item 95 : 95-95
13FM ; Item 96 : 96-96
13FD ; Item 97 : 97-97
END NAMES
313 1- 4 1 43   22 1-   11 31 3 1  31 2 1   32 12111  23i  1 32   2i111  1231- 2 1   2321 2322112 1 Sashi Cheliah
323 32   1 41 3 1  331   2232   21 531  22--23     23 1- 2 2332   233-     2342  321 1-  11211222 2 Ben Borsht
313 32   1 43   23332    1 32   21 1- 112i--32 112 1  32   211- 121-122    231 1221  21 2  1-3    3 Khanh Ong
326132   1 33   1  32    1 31 1222342   242233     21 231  1 332  2411 2   1241  3221231 2 23     4 Jess Liemantara
312 31 121 441  1  332   2432   222531  1   33     22 31 4 22331  1-21 1 21-3s   21  223          5 Chloe Carroll
313 32   2132   22 21 1  1 32   1  51 2 1   31 2   1  1- 3 1 32   1-11  2  i22   3222             6 Reece Hignell
313 341  1 43   23131  2 2321 4 1  51 2 1   33     1  32   2221 3 2211  13 3333                   7 Samira Damirova
313 31 2 1 1- 3 21 32    2322   1  52   1   33     1  31 121 21 3 2113     4                      8 Kristen Sheffield
313 22   2143   1  22    1 331  224                  132   2131 2 25                              9 Brendan Pang (16)
313 32   1 43   22 22    241- 2 22122   1   342    22 231  1 333                                  10 Sarah Clare
313 32   1 41 2 23132    1 32   1  532  2421341    1  32   24                                     11 Hoda Kobeissi
311 22   2233   1  22    2332   1  52   1   1- 13  22 332                                         12* Gina Ottaway
312 32   2143   1  32    2331 5 21 52   231-23     243                                            12 Aldo Ortado
323 32   2242   21 32    1 233  1  52   21--343      2                                            13 Lisa Diep
323 32   23442  1  32    1 332  21 51 2 2323         3                                            14 Jenny Lam
315222   2223   23232    1 22   1  333               3                                            15 Genene Dwyer
314 32   2243   1  32    21334                       3                                            17 Jo Kendray
312 32   1 41 111  32    25                          3                                            18 Loki Madireddi (i)
333 332  1 43   1  333                               2                                            19 Michelle Walsh
323 31 3 2243   234                                  4                                            20 Tim Talam
313 32   23443                                       4                                            21 Adele Elliott
313 22   24                                          4                                            22 Denise Valdez
313 343                                              3                                            23 Metter Chin
3153                                                 4                                            24 Brett McGrath
2       1      2      212      1       2          2       2      1              1                 Guest Chef
4                                                         3                                     3 Minimum at 0
1                                                         1                                     1 Maximum at 100

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