implement.MSPRT: Implementing the MSPRT
In MSPRT: A Modified Sequential Probability Ratio Test (MSPRT)
Description
Usage
Arguments
Details
Value
Author(s)
References
Examples
Description
This function implements the MSPRT for a sequentially observed data.
Usage
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implement.MSPRT(obs, obs1, obs2, design.MSPRT.object,
termination.threshold, test.type, side = "right",
theta0, Type1.target = 0.005, Type2.target = 0.2,
N.max, N1.max, N2.max,
sigma = 1, sigma1 = 1, sigma2 = 1,
batch.size, batch1.size, batch2.size,
verbose = T, plot.it = 2)
Arguments
obs
Numeric vector. The vector of data in the order they are sequentially observed for one-sample tests.
Note: Its length can't exceed the length of batch.size.
obs1
Numeric vector. The vector of data in the order they are sequentially observed from Group-1 for two-sample tests.
Note: Its length can't exceed the length of batch1.size.
obs2
Numeric vector. The vector of data in the order they are sequentially observed from Group-2 for two-sample tests.
Note: Its length can't exceed the length of batch2.size.
design.MSPRT.object
List. The output returned from design.MSPRT corresponding to the MSPRT for which the operating characteristics are desired.
termination.threshold
Positive numeric. Termination threshold of the designed MSPRT.
test.type
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
side
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
theta0
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
Type1.target
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
Type2.target
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
N.max
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
N1.max
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
N2.max
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
sigma
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
sigma1
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
sigma2
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
batch.size
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
batch1.size
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
batch2.size
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
verbose
Logical. If TRUE (default), returns messages of the current proceedings. Otherwise it doesn't.
plot.it
0, 1 or 2 (default).
if plot.it=0, no plot is returned.
if plot.it=1, only the ggplot object required to get a comparison plot is returned, but it's not plotted.
if plot.it=2, a comparison plot and the corresponding ggplot object is returned.
Details
If design.MSPRT.object is provided, one can only additionally provide nReplicate, nCore, verbose and seed (Easier option). Otherwise, just like in design.MSPRT, all the other arguments together with termination.threshold (obtained from design.MSPRT) needs to be provided adequately.
Value
List. The list has the following named components in case of one-sided one-sample tests:
n
Positive integer. Number of samples required to reach the decision.
decision
Character. The decision reached. The possibilities are 'accept', 'reject' and 'continue'. They respectively correspond to accepting H_0, rejecting H_0 and continue sampling.
RejectH0.threshold
Positive numeric. Threshold for rejecting H_0 in the MSPRT.
RejectH1.threshold
Positive numeric. Threshold for accepting H_1 in the MSPRT.
LR
Numeric vector. Vector of weighted likelihood ratios (proportion tests) or likelihood ratios (z tests) or Bayes factor (t tests) that are computed at each step of sequential analysis until either a decision is reached or the maximum available number of samples (N.max in one-sample tests, or N1.max and N2.max in two-sample tests) has been used.
UMPBT alternative
This stores the UMPBT alternative(s) as
-
UMPBT for proportion tests. Of the same type as it is returned by UMPBT.alt in these tests.
-
theta.UMPBT for z and t tests. This is a numeric in case of z tests and a numeric vector in case of t tests. For t tests the UMPBT alternative depends on the data. So the numeric vector returned in this case contains the UMPBT alternative computed at step of sequential analysis and is based on all data observed until that step.
In case of two-sample tests, the n output above is replaced by n1 and n2. They are positive integers and refer to the number of samples from Group-1 and 2 required to reach the decision.
In case of two-sided tests at level of significance α, the MSPRT carries out a right and a left sided test simultaneously at level of significance α/2. In this case the outputs are same as above with following changes in components in the returned list:
LR
List. It has two components named right and left corresponding to the right and left sided tests of size α/2. Each of these components stores the vector of weighted likelihood ratios (proportion tests) or likelihood ratios (z tests) or Bayes factor (t tests) that are computed at each step of sequential analysis until either a decision is reached or the maximum available number of samples (N.max in one-sample tests, or N1.max and N2.max in two-sample tests) has been used for that sided test.
UMPBT or theta.UMPBT
List with two components named right and left corresponding to the right and left sided tests of size α/2. Each of these contains the UMPBT alternative (of the same type as the output from UMPBT.alt for the test with respective sides.
Author(s)
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
References
Pramanik S., Johnson V. E. and Bhattacharya A. (2020+). A Modified Sequential Probability Ratio Test. [Arxiv]
Examples
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#################### one-sample proportion test ####################
#### right sided ####
### design
#design.oneprop.right = design.MSPRT(test.type = 'oneProp', side = 'right',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0.5 # change effect size to experiment
#y = rbinom(20, 1, theta.gen)
#implement.oneprop.right = implement.MSPRT(obs = y,
# design.MSPRT.object = design.oneprop.right)
#### left sided ####
### design
#design.oneprop.left = design.MSPRT(test.type = 'oneProp', side = 'left',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0.5 # change effect size to experiment
#y = rbinom(20, 1, theta.gen)
#implement.oneprop.left = implement.MSPRT(obs = y,
# design.MSPRT.object = design.oneprop.left)
#### both sided ####
### design
#design.oneprop.both = design.MSPRT(test.type = 'oneProp', side = 'both',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0.5 # change effect size to experiment
#y = rbinom(20, 1, theta.gen)
#implement.oneprop.both = implement.MSPRT(obs = y,
# design.MSPRT.object = design.oneprop.both)
#################### one-sample z test ####################
#### right sided ####
### design
#design.onez.right = design.MSPRT(test.type = 'oneZ', side = 'right',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y = rnorm(20, theta.gen, design.onez.right$sigma)
#implement.onez.right = implement.MSPRT(obs = y,
# design.MSPRT.object = design.onez.right)
#### left sided ####
### design
#design.onez.left = design.MSPRT(test.type = 'oneZ', side = 'left',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y = rnorm(20, theta.gen, design.onez.left$sigma)
#implement.onez.left = implement.MSPRT(obs = y,
# design.MSPRT.object = design.onez.left)
#### both sided ####
### design
#design.onez.both = design.MSPRT(test.type = 'oneZ', side = 'both',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y = rnorm(20, theta.gen, design.onez.both$sigma)
#implement.onez.both = implement.MSPRT(obs = y,
# design.MSPRT.object = design.onez.both)
#################### one-sample t test ####################
#### right sided ####
### design
#design.onet.right = design.MSPRT(test.type = 'oneT', side = 'right',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y = rnorm(20, theta.gen, 1)
#implement.onet.right = implement.MSPRT(obs = y,
# design.MSPRT.object = design.onet.right)
#### left sided ####
### design
#design.onet.left = design.MSPRT(test.type = 'oneT', side = 'left',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y = rnorm(20, theta.gen, 1)
#implement.onet.left = implement.MSPRT(obs = y,
# design.MSPRT.object = design.onet.left)
#### both sided ####
### design
#design.onet.both = design.MSPRT(test.type = 'oneT', side = 'both',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y = rnorm(20, theta.gen, 1)
#implement.onet.both = implement.MSPRT(obs = y,
# design.MSPRT.object = design.onet.both)
#################### two-sample z test ####################
#### right sided ####
### design
#design.twoz.right = design.MSPRT(test.type = 'twoZ', side = 'right',
# N1.max = 20, N2.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y1 = rnorm(20, theta.gen/2, design.twoz.right$sigma1)
#y2 = rnorm(20, -theta.gen/2, design.twoz.right$sigma2)
#implement.twoz.right = implement.MSPRT(obs1 = y1, obs2 = y2,
# design.MSPRT.object = design.twoz.right)
#### left sided ####
### design
#design.twoz.left = design.MSPRT(test.type = 'twoZ', side = 'left',
# N1.max = 20, N2.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y1 = rnorm(20, theta.gen/2, design.twoz.left$sigma1)
#y2 = rnorm(20, -theta.gen/2, design.twoz.left$sigma2)
#implement.twoz.left = implement.MSPRT(obs1 = y1, obs2 = y2,
# design.MSPRT.object = design.twoz.left)
#### both sided ####
### design
#design.twoz.both = design.MSPRT(test.type = 'twoZ', side = 'both',
# N1.max = 20, N2.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y1 = rnorm(20, theta.gen/2, design.twoz.both$sigma1)
#y2 = rnorm(20, -theta.gen/2, design.twoz.both$sigma2)
#implement.twoz.both = implement.MSPRT(obs1 = y1, obs2 = y2,
# design.MSPRT.object = design.twoz.both)
#################### two-sample t test ####################
#### right sided ####
### design
#design.twot.right = design.MSPRT(test.type = 'twoT', side = 'right',
# N1.max = 20, N2.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y1 = rnorm(20, theta.gen/2, 1)
#y2 = rnorm(20, -theta.gen/2, 1)
#implement.twot.right = implement.MSPRT(obs1 = y1, obs2 = y2,
# design.MSPRT.object = design.twot.right)
#### left sided ####
### design
#design.twot.left = design.MSPRT(test.type = 'twoT', side = 'left',
# N1.max = 20, N2.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y1 = rnorm(20, theta.gen/2, 1)
#y2 = rnorm(20, -theta.gen/2, 1)
#implement.twot.left = implement.MSPRT(obs1 = y1, obs2 = y2,
# design.MSPRT.object = design.twot.left)
#### both sided ####
### design
#design.twot.both = design.MSPRT(test.type = 'twoT', side = 'both',
# N1.max = 20, N2.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y1 = rnorm(20, theta.gen/2, 1)
#y2 = rnorm(20, -theta.gen/2, 1)
#implement.twot.both = implement.MSPRT(obs1 = y1, obs2 = y2,
# design.MSPRT.object = design.twot.both)
MSPRT documentation built on Nov. 13, 2020, 5:07 p.m.
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Description Usage Arguments Details Value Author(s) References Examples
Description
This function implements the MSPRT for a sequentially observed data.
Usage
1 2 3 4 5 6 7 | implement.MSPRT(obs, obs1, obs2, design.MSPRT.object,
termination.threshold, test.type, side = "right",
theta0, Type1.target = 0.005, Type2.target = 0.2,
N.max, N1.max, N2.max,
sigma = 1, sigma1 = 1, sigma2 = 1,
batch.size, batch1.size, batch2.size,
verbose = T, plot.it = 2)
|
Arguments
obs |
Numeric vector. The vector of data in the order they are sequentially observed for one-sample tests.
Note: Its length can't exceed the length of |
obs1 |
Numeric vector. The vector of data in the order they are sequentially observed from Group-1 for two-sample tests.
Note: Its length can't exceed the length of |
obs2 |
Numeric vector. The vector of data in the order they are sequentially observed from Group-2 for two-sample tests.
Note: Its length can't exceed the length of |
design.MSPRT.object |
List. The output returned from |
termination.threshold |
Positive numeric. Termination threshold of the designed MSPRT. |
test.type |
Same as in |
side |
Same as in |
theta0 |
Same as in |
Type1.target |
Same as in |
Type2.target |
Same as in |
N.max |
Same as in |
N1.max |
Same as in |
N2.max |
Same as in |
sigma |
Same as in |
sigma1 |
Same as in |
sigma2 |
Same as in |
batch.size |
Same as in |
batch1.size |
Same as in |
batch2.size |
Same as in |
verbose |
Logical. If TRUE (default), returns messages of the current proceedings. Otherwise it doesn't. |
plot.it |
0, 1 or 2 (default).
|
Details
If design.MSPRT.object is provided, one can only additionally provide nReplicate, nCore, verbose and seed (Easier option). Otherwise, just like in design.MSPRT, all the other arguments together with termination.threshold (obtained from design.MSPRT) needs to be provided adequately.
Value
List. The list has the following named components in case of one-sided one-sample tests:
n |
Positive integer. Number of samples required to reach the decision. |
decision |
Character. The decision reached. The possibilities are |
RejectH0.threshold |
Positive numeric. Threshold for rejecting H_0 in the MSPRT. |
RejectH1.threshold |
Positive numeric. Threshold for accepting H_1 in the MSPRT. |
LR |
Numeric vector. Vector of weighted likelihood ratios (proportion tests) or likelihood ratios (z tests) or Bayes factor (t tests) that are computed at each step of sequential analysis until either a decision is reached or the maximum available number of samples ( |
UMPBT alternative |
This stores the UMPBT alternative(s) as
|
In case of two-sample tests, the n output above is replaced by n1 and n2. They are positive integers and refer to the number of samples from Group-1 and 2 required to reach the decision.
In case of two-sided tests at level of significance α, the MSPRT carries out a right and a left sided test simultaneously at level of significance α/2. In this case the outputs are same as above with following changes in components in the returned list:
LR |
List. It has two components named |
UMPBT or theta.UMPBT |
List with two components named |
Author(s)
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
References
Pramanik S., Johnson V. E. and Bhattacharya A. (2020+). A Modified Sequential Probability Ratio Test. [Arxiv]
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 | #################### one-sample proportion test ####################
#### right sided ####
### design
#design.oneprop.right = design.MSPRT(test.type = 'oneProp', side = 'right',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0.5 # change effect size to experiment
#y = rbinom(20, 1, theta.gen)
#implement.oneprop.right = implement.MSPRT(obs = y,
# design.MSPRT.object = design.oneprop.right)
#### left sided ####
### design
#design.oneprop.left = design.MSPRT(test.type = 'oneProp', side = 'left',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0.5 # change effect size to experiment
#y = rbinom(20, 1, theta.gen)
#implement.oneprop.left = implement.MSPRT(obs = y,
# design.MSPRT.object = design.oneprop.left)
#### both sided ####
### design
#design.oneprop.both = design.MSPRT(test.type = 'oneProp', side = 'both',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0.5 # change effect size to experiment
#y = rbinom(20, 1, theta.gen)
#implement.oneprop.both = implement.MSPRT(obs = y,
# design.MSPRT.object = design.oneprop.both)
#################### one-sample z test ####################
#### right sided ####
### design
#design.onez.right = design.MSPRT(test.type = 'oneZ', side = 'right',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y = rnorm(20, theta.gen, design.onez.right$sigma)
#implement.onez.right = implement.MSPRT(obs = y,
# design.MSPRT.object = design.onez.right)
#### left sided ####
### design
#design.onez.left = design.MSPRT(test.type = 'oneZ', side = 'left',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y = rnorm(20, theta.gen, design.onez.left$sigma)
#implement.onez.left = implement.MSPRT(obs = y,
# design.MSPRT.object = design.onez.left)
#### both sided ####
### design
#design.onez.both = design.MSPRT(test.type = 'oneZ', side = 'both',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y = rnorm(20, theta.gen, design.onez.both$sigma)
#implement.onez.both = implement.MSPRT(obs = y,
# design.MSPRT.object = design.onez.both)
#################### one-sample t test ####################
#### right sided ####
### design
#design.onet.right = design.MSPRT(test.type = 'oneT', side = 'right',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y = rnorm(20, theta.gen, 1)
#implement.onet.right = implement.MSPRT(obs = y,
# design.MSPRT.object = design.onet.right)
#### left sided ####
### design
#design.onet.left = design.MSPRT(test.type = 'oneT', side = 'left',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y = rnorm(20, theta.gen, 1)
#implement.onet.left = implement.MSPRT(obs = y,
# design.MSPRT.object = design.onet.left)
#### both sided ####
### design
#design.onet.both = design.MSPRT(test.type = 'oneT', side = 'both',
# N.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y = rnorm(20, theta.gen, 1)
#implement.onet.both = implement.MSPRT(obs = y,
# design.MSPRT.object = design.onet.both)
#################### two-sample z test ####################
#### right sided ####
### design
#design.twoz.right = design.MSPRT(test.type = 'twoZ', side = 'right',
# N1.max = 20, N2.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y1 = rnorm(20, theta.gen/2, design.twoz.right$sigma1)
#y2 = rnorm(20, -theta.gen/2, design.twoz.right$sigma2)
#implement.twoz.right = implement.MSPRT(obs1 = y1, obs2 = y2,
# design.MSPRT.object = design.twoz.right)
#### left sided ####
### design
#design.twoz.left = design.MSPRT(test.type = 'twoZ', side = 'left',
# N1.max = 20, N2.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y1 = rnorm(20, theta.gen/2, design.twoz.left$sigma1)
#y2 = rnorm(20, -theta.gen/2, design.twoz.left$sigma2)
#implement.twoz.left = implement.MSPRT(obs1 = y1, obs2 = y2,
# design.MSPRT.object = design.twoz.left)
#### both sided ####
### design
#design.twoz.both = design.MSPRT(test.type = 'twoZ', side = 'both',
# N1.max = 20, N2.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y1 = rnorm(20, theta.gen/2, design.twoz.both$sigma1)
#y2 = rnorm(20, -theta.gen/2, design.twoz.both$sigma2)
#implement.twoz.both = implement.MSPRT(obs1 = y1, obs2 = y2,
# design.MSPRT.object = design.twoz.both)
#################### two-sample t test ####################
#### right sided ####
### design
#design.twot.right = design.MSPRT(test.type = 'twoT', side = 'right',
# N1.max = 20, N2.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y1 = rnorm(20, theta.gen/2, 1)
#y2 = rnorm(20, -theta.gen/2, 1)
#implement.twot.right = implement.MSPRT(obs1 = y1, obs2 = y2,
# design.MSPRT.object = design.twot.right)
#### left sided ####
### design
#design.twot.left = design.MSPRT(test.type = 'twoT', side = 'left',
# N1.max = 20, N2.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y1 = rnorm(20, theta.gen/2, 1)
#y2 = rnorm(20, -theta.gen/2, 1)
#implement.twot.left = implement.MSPRT(obs1 = y1, obs2 = y2,
# design.MSPRT.object = design.twot.left)
#### both sided ####
### design
#design.twot.both = design.MSPRT(test.type = 'twoT', side = 'both',
# N1.max = 20, N2.max = 20)
### implementation
#set.seed(1)
#theta.gen = 0 # change effect size to experiment
#y1 = rnorm(20, theta.gen/2, 1)
#y2 = rnorm(20, -theta.gen/2, 1)
#implement.twot.both = implement.MSPRT(obs1 = y1, obs2 = y2,
# design.MSPRT.object = design.twot.both)
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