Generate a single-case design matrix

Generates a parameter list used for generating multiple random single-cases. This is used within the random_scdf function and the power_test function and for other Monte-Carlo tasks.

Usage

design(
  n = 1,
  phase_design = list(A = 5, B = 15),
  trend = 0,
  level = list(0),
  slope = list(0),
  start_value = 50,
  s = 10,
  rtt = 0.8,
  extreme_prop = list(0),
  extreme_range = c(-4, -3),
  missing_prop = 0,
  distribution = c("normal", "gaussian", "poisson", "binomial"),
  random_start_value = FALSE,
  n_trials = NULL,
  mt = NULL,
  B_start = NULL,
  m,
  phase.design,
  MT,
  B.start,
  extreme.p,
  extreme.d,
  missing.p
)

Arguments

n: Number of cases to be designed (Default is n = 1).
phase_design, phase.design: A list defining the length and label of each phase. E.g., phase.length = list(A1 = 10, B1 = 10, A2 = 10, B2 = 10). Use vectors if you want to define different values for each case phase.length = list(A = c(10, 15), B = c(10, 15).
trend: Defines the effect size of a trend added incrementally to each measurement across the whole data-set. To assign different trends to several single-cases, use a vector of values (e.g. trend = c(.1, .3, .5)). If the number of cases exceeds the length of the vector, values are recycled. When using a 'gaussian' distribution, the trend parameters indicate effect size d changes. When using a binomial or poisson distribution, trend indicates an increase in points / counts per measurement.
level: A list that defines the level increase (effect size d) at the beginning of each phase relative to the previous phase (e.g. list(A = 0, B = 1)). The first element must be zero as the first phase of a single-case has no level effect (if you have one less list element than the number of phases, scan will add a leading element with 0 values). Use vectors to define variable level effects for each case (e.g. list(A = c(0, 0), B = c(1, 2))). When using a 'gaussian' distribution, the level parameters indicate effect size d changes. When using a binomial or poisson distribution, level indicates an increase in points / counts with the onset of each phase.
slope: A list that defines the increase per measurement for each phase compared to the previous phase. slope = list(A = 0, B = .1) generates an incremental increase of 0.1 per measurement starting at the B phase. The first list element must be zero as the first phase of a single-case has no slope effect (if you have one less list element than the number of phases, scan will add a leading element with 0 values). Use vectors to define variable slope effects for each case (e.g. list(A = c(0, 0), B = c(0.1, 0.2))). If the number of cases exceeds the length of the vector, values are recycled. When using a 'gaussian' distribution, the slope parameters indicate effect size d changes per measurement. When using a binomial or poisson distribution, slope indicates an increase in points / counts per measurement.
start_value, m: Starting value at the first measurement. Default is 50. When distribution = "poission" the start_value represents frequency. When distribution = "binomial" start_value must range between 0 and 1 and they represent the probability of on event. To assign different start values to several single-cases, use a vector of values (e.g. c(50, 42, 56)). If the number of cases exceeds the length of the vector, values are recycled. The m argument is deprecated.
s: Standard deviation used to calculate absolute values from level, slope, trend effects and to calculate and error distribution from the rtt values. Set to 10 by default. To assign different variances to several single-cases, use a vector of values (e.g. s = c(5, 10, 15)). If the number of cases exceeds the length of the vector, values are recycled. if the distribution is 'poisson' or 'binomial' s is not applied.
rtt: Reliability of the underlying simulated measurements. Set rtt = .8 by default. To assign different reliabilities to several single-cases, use a vector of values (e.g. rtt = c(.6, .7, .8)). If the number of cases exceeds the length of the vector, values are repeated. rtt has no effect when you're using binomial or poisson distributions.
extreme_prop, extreme.p: Probability of extreme values. extreme.p = .05 gives a five percent probability of an extreme value. A vector of values assigns different probabilities to multiple cases. If the number of cases exceeds the length of the vector, values are recycled.
extreme_range, extreme.d: Range for extreme values. extreme_range = c(-7,-6) uses extreme values within a range of -7 and -6 . In case of a binomial or poisson distribution, extreme_range indicates frequencies. In case of a gaussian (or normal) distribution it indicates effect size d. Caution: the first value must be smaller than the second, otherwise the procedure will fail.
missing_prop, missing.p: Portion of missing values. missing_prop = 0.1 creates 10\ different probabilities to multiple cases. If the number of cases exceeds the length of the vector, values are repeated.
distribution: Distribution of the criteria varible. Default is "normal". Possible values are "normal", "binomial", and "poisson".
random_start_value: If TRUE, the start_values are randomized based on the distribution.
n_trials: If distribution (see below) is "binomial", n_trials is the number of trials/observations/items.
mt, MT: Number of measurements (in each study). Default is mt = 20.
B_start, B.start: Phase B starting point. The default setting B_start = 6 would assign the first five scores (of each case) to phase A, and all following scores to phase B. To assign different starting points for a set of multiple single-cases, use a vector of starting values (e.g., B_start = c(6, 7, 8)). If the number of cases exceeds the length of the vector, values will be recycled.

Value

An object of class sc_design.

Author

Juergen Wibert

Examples

 ## Create random single-case data and inspect it
 design <- design(
   n = 3, rtt = 0.75, slope = 0.1, extreme_prop = 0.1,
   missing_prop = 0.1
 )
 dat <- random_scdf(design, round = 1, random.names = TRUE, seed = 123)
 describe(dat)
#> Describe Single-Case Data
#> 
#>        Case1 Case2 Case3
#> Design   A-B   A-B   A-B
#> n.A        5     5     5
#> n.B       15    15    15
#> mis.A      0     1     0
#> mis.B      2     1     2
#> 
#>          Case1  Case2  Case3
#> m.A      51.12  50.00  54.36
#> m.B     57.115 52.793 56.892
#> md.A      50.4   49.2   52.6
#> md.B     59.60  55.75  59.20
#> sd.A     4.672  3.631  4.538
#> sd.B    10.403 12.893  8.003
#> mad.A    2.520  2.076  3.410
#> mad.B    7.858 10.601  6.672
#> min.A     46.8   46.5   50.3
#> min.B     29.7   19.7   38.7
#> max.A     59.0   55.1   61.8
#> max.B     71.3   65.2   67.7
#> trend.A   0.95   1.36   2.27
#> trend.B  0.935  1.693  1.358

 ## And now have a look at poisson-distributed data
 design <- design(
   n = 3, B_start = c(6, 10, 14), mt = c(12, 20, 22), start_value = 10,
   distribution = "poisson", level = -5, missing_prop = 0.1
 )
 dat <- random_scdf(design, seed = 1234)
 pand(dat, decreasing = TRUE)
#> Percentage of all non-overlapping data
#> 
#> Method: sort 
#> 
#> PAND = 91.8%
#> Φ =  0.836  ; Φ² =  0.699 
#> 
#> 49 measurements (23 Phase A, 26 Phase B) in 3 cases
#> Overlapping data: n = 4 ; percentage = 8.2 
#> 
#> 2 x 2 Matrix of percentages
#>          A    B total
#> A     42.9  4.1  46.9
#> B      4.1 49.0  53.1
#> total 46.9 53.1 100.0
#> 
#> 2 x 2 Matrix of counts
#>        A  B total
#> A     21  2    23
#> B      2 24    26
#> total 23 26    49
#> 
#> 
#> Chi-Squared test:
#> X² = 34.256, df = 1, p = 0.000 
#> 
#> Fisher exact test:
#> Odds ratio = 99.881, p = 0.000