Original Values

• The original values from the combine data set

No. of redistributions

• Because the gamma distribution created some extremely high numbers we end up redistributin anyone who scored higher than 80 Standardard drinks. These two plots represent the number of mean times this occured at a given level of a simulation and the max times it occurred. The total number of cells in the data set was 80640 therefore even though this occurred it was only for a small number of the total data set.

Simulation Plots

• I simulated 6 different levels of mode (range = 1.0 to 1.5) and 10 different levels of SD (range = 0.0 to 0.14)both have an impact on the mean of the drinking bias (X axis). There are 1000 simulations at each combination of levels of mode and SD (each point on the graph) for a total of 90000 simulations.
• The black horizontal line on each point represents the value of the original COMBINE data set (N = 896; after removing 487 subjects due to missigness)

Drink Bias Plots

• These are profiles of the drink bias distributions we used for each level of the simulation. These are based on a gamma distribution which is parameterized by two different parameters (shape and rate). However, one can convert a mode and SD of a distribution into a shape and rate parameters.
• \(rate = ( mode + sqrt( mode^2 + 4*sd^2 ) ) / ( 2 * sd^2 )\)
• \(shape = 1 + mode * rate\)

Selecting parameters for simulation

    Mode   SD Mean Plot.Number
1    1.0 0.01 1.00           1
2    1.0 0.11 1.01           2
3    1.0 0.21 1.04           3
4    1.0 0.31 1.09           4
16   1.1 0.01 1.10          16
17   1.1 0.11 1.11          17
18   1.1 0.21 1.13          18
5    1.0 0.41 1.14           5
19   1.1 0.31 1.17          19
31   1.2 0.01 1.20          31
6    1.0 0.51 1.21           6
32   1.2 0.11 1.21          32
20   1.1 0.41 1.24          20
33   1.2 0.21 1.25          33
34   1.2 0.31 1.29          34
7    1.0 0.61 1.30           7
21   1.1 0.51 1.30          21
46   1.3 0.01 1.30          46
47   1.3 0.11 1.31          47
35   1.2 0.41 1.33          35
48   1.3 0.21 1.33          48
22   1.1 0.61 1.37          22
36   1.2 0.51 1.37          36
8    1.0 0.71 1.38           8
49   1.3 0.31 1.38          49
61   1.4 0.01 1.40          61
50   1.3 0.41 1.41          50
62   1.4 0.11 1.41          62
63   1.4 0.21 1.43          63
9    1.0 0.81 1.45           9
37   1.2 0.61 1.45          37
64   1.4 0.31 1.47          64
23   1.1 0.71 1.48          23
51   1.3 0.51 1.49          51
24   1.1 0.81 1.50          24
76   1.5 0.01 1.50          76
38   1.2 0.71 1.51          38
77   1.5 0.11 1.51          77
65   1.4 0.41 1.52          65
52   1.3 0.61 1.53          52
78   1.5 0.21 1.54          78
66   1.4 0.51 1.55          66
79   1.5 0.31 1.55          79
10   1.0 0.91 1.56          10
53   1.3 0.71 1.60          53
80   1.5 0.41 1.60          80
91   1.6 0.01 1.60          91
92   1.6 0.11 1.61          92
11   1.0 1.01 1.62          11
25   1.1 0.91 1.62          25
39   1.2 0.81 1.62          39
67   1.4 0.61 1.64          67
93   1.6 0.21 1.64          93
94   1.6 0.31 1.65          94
81   1.5 0.51 1.66          81
54   1.3 0.81 1.67          54
26   1.1 1.01 1.68          26
95   1.6 0.41 1.69          95
68   1.4 0.71 1.70          68
106  1.7 0.01 1.70         106
107  1.7 0.11 1.71         107
40   1.2 0.91 1.72          40
82   1.5 0.61 1.72          82
12   1.0 1.11 1.73          12
108  1.7 0.21 1.73         108
96   1.6 0.51 1.75          96
55   1.3 0.91 1.76          55
109  1.7 0.31 1.76         109
83   1.5 0.71 1.77          83
110  1.7 0.41 1.78         110
27   1.1 1.11 1.79          27
97   1.6 0.61 1.79          97
69   1.4 0.81 1.80          69
121  1.8 0.01 1.80         121
41   1.2 1.01 1.81          41
122  1.8 0.11 1.81         122
123  1.8 0.21 1.82         123
84   1.5 0.81 1.83          84
111  1.7 0.51 1.84         111
124  1.8 0.31 1.86         124
13   1.0 1.21 1.87          13
42   1.2 1.11 1.87          42
70   1.4 0.91 1.87          70
98   1.6 0.71 1.87          98
56   1.3 1.01 1.88          56
14   1.0 1.31 1.89          14
57   1.3 1.11 1.89          57
28   1.1 1.21 1.90          28
125  1.8 0.41 1.90         125
136  1.9 0.01 1.90         136
112  1.7 0.61 1.91         112
137  1.9 0.11 1.91         137
138  1.9 0.21 1.92         138
99   1.6 0.81 1.93          99
71   1.4 1.01 1.94          71
126  1.8 0.51 1.94         126
113  1.7 0.71 1.95         113
139  1.9 0.31 1.95         139
43   1.2 1.21 1.96          43
85   1.5 0.91 1.96          85
29   1.1 1.31 1.97          29
127  1.8 0.61 1.99         127
140  1.9 0.41 1.99         140
72   1.4 1.11 2.00          72
86   1.5 1.01 2.00          86
100  1.6 0.91 2.00         100
151  2.0 0.01 2.00         151
128  1.8 0.71 2.01         128
152  2.0 0.11 2.01         152
44   1.2 1.31 2.02          44
153  2.0 0.21 2.02         153
141  1.9 0.51 2.03         141
58   1.3 1.21 2.04          58
154  2.0 0.31 2.04         154
114  1.7 0.81 2.05         114
101  1.6 1.01 2.06         101
30   1.1 1.41 2.07          30
155  2.0 0.41 2.08         155
59   1.3 1.31 2.09          59
73   1.4 1.21 2.09          73
129  1.8 0.81 2.09         129
15   1.0 1.41 2.10          15
45   1.2 1.41 2.10          45
142  1.9 0.61 2.11         142
74   1.4 1.31 2.12          74
87   1.5 1.11 2.12          87
115  1.7 0.91 2.12         115
143  1.9 0.71 2.14         143
156  2.0 0.51 2.14         156
130  1.8 0.91 2.15         130
102  1.6 1.11 2.16         102
116  1.7 1.01 2.16         116
157  2.0 0.61 2.17         157
88   1.5 1.21 2.18          88
60   1.3 1.41 2.21          60
103  1.6 1.21 2.21         103
144  1.9 0.81 2.21         144
158  2.0 0.71 2.21         158
131  1.8 1.01 2.26         131
75   1.4 1.41 2.27          75
117  1.7 1.11 2.27         117
145  1.9 0.91 2.27         145
89   1.5 1.31 2.28          89
118  1.7 1.21 2.29         118
159  2.0 0.81 2.30         159
104  1.6 1.31 2.31         104
160  2.0 0.91 2.33         160
132  1.8 1.11 2.34         132
146  1.9 1.01 2.34         146
105  1.6 1.41 2.38         105
161  2.0 1.01 2.39         161
90   1.5 1.41 2.41          90
119  1.7 1.31 2.41         119
133  1.8 1.21 2.43         133
147  1.9 1.11 2.44         147
134  1.8 1.31 2.49         134
162  2.0 1.11 2.51         162
148  1.9 1.21 2.52         148
163  2.0 1.21 2.54         163
120  1.7 1.41 2.56         120
135  1.8 1.41 2.56         135
150  1.9 1.41 2.58         150
149  1.9 1.31 2.60         149
164  2.0 1.31 2.66         164
165  2.0 1.41 2.79         165