This functions takes an scdf and extracts design parameters. The resulting object can be used to randomly create new scdf files with the same underlying parameters. This is useful for Monte-Carlo studies and bootstrapping procedures.
Usage
estimate_design(
data,
dvar,
pvar,
mvar,
s = NULL,
rtt = NULL,
overall_effects = FALSE,
overall_rtt = TRUE,
model = "JW",
...
)Arguments
- data
A single-case data frame. See
scdf()to learn about this format.- dvar
Character string with the name of the dependent variable. Defaults to the attributes in the scdf file.
- pvar
Character string with the name of the phase variable. Defaults to the attributes in the scdf file.
- mvar
Character string with the name of the measurement time variable. Defaults to the attributes in the scdf file.
- s
The standard deviation depicting the between case variance of the overall performance. If more than two single-cases are included in the scdf, the variance is estimated if s is set to NULL.
- rtt
The reliability of the measurements. The reliability is estimated when rtt = NULL.
- overall_effects
If TRUE, trend, level, and slope effect estimations will be identical for each case. If FALSE, effects are estimated for each case separately.
- overall_rtt
Ignored when
rttis set. If TRUE, rtt estimations will be based on all cases and identical for each case. If FALSE rtt is estimated for each case separately.- model
Model used for calculating the dummy parameters (see Huitema & McKean, 2000). Default is
model = "W". Possible values are:"B&L-B","H-M","W", and deprecated"JW".- ...
Further arguments passed to the plm function used for parameter estimation.
Value
A list of parameters for each single-case. Parameters include name, length, and starting measurement time of each phase, trend, level, and slope effects for each phase, start value, standard deviation, and reliability for each case.
Examples
# create a random scdf with predefined parameters
set.seed(1234)
design <- design(
n = 10, trend = -0.02,
level = list(0, 1), rtt = 0.8,
s = 1
)
scdf<- random_scdf(design)
# Estimate the parameters based on the scdf and create a new random scdf
# based on these estimations
design_est <- estimate_design(scdf, rtt = 0.8)
scdf_est <- random_scdf(design_est)
# Analyze both datasets with an hplm model. See how similar the estimations
# are:
hplm(scdf, slope = FALSE)
#> Hierarchical Piecewise Linear Regression
#>
#> Estimation method ML
#> Contrast model: W / level: first, slope: first
#> 10 Cases
#>
#> ICC = 0.004; L = 0.0; p = 0.870
#>
#> Fixed effects (values ~ 1 + mt + phaseB)
#>
#> B SE df t p
#> Intercept 50.004 0.079 188 633.489 0.000
#> Trend mt -0.024 0.009 188 -2.579 0.011
#> Level phase B 1.010 0.125 188 8.088 0.000
#>
#> Random effects (~1 | case)
#>
#> EstimateSD
#> Intercept 0.088
#> Residual 0.501
hplm(scdf_est, slope = FALSE)
#> Hierarchical Piecewise Linear Regression
#>
#> Estimation method ML
#> Contrast model: W / level: first, slope: first
#> 10 Cases
#>
#> ICC = 0.071; L = 5.4; p = 0.020
#>
#> Fixed effects (values ~ 1 + mt + phaseB)
#>
#> B SE df t p
#> Intercept 50.068 0.120 188 416.805 0.000
#> Trend mt -0.028 0.012 188 -2.254 0.025
#> Level phase B 1.011 0.165 188 6.125 0.000
#>
#> Random effects (~1 | case)
#>
#> EstimateSD
#> Intercept 0.220
#> Residual 0.662
# Also similar results for pand and randomization tests:
pand(scdf)
#> Percentage of all non-overlapping data
#>
#> Method: sort
#>
#> PAND = 84%
#> Φ = 0.573 ; Φ² = 0.329
#>
#> 200 measurements (50 Phase A, 150 Phase B) in 10 cases
#> Overlapping data: n = 32 ; percentage = 16
#>
#> 2 x 2 Matrix of percentages
#> A B total
#> A 17 8 25
#> B 8 67 75
#> total 25 75 100
#>
#> 2 x 2 Matrix of counts
#> A B total
#> A 34 16 50
#> B 16 134 150
#> total 50 150 200
#>
#>
#> Chi-Squared test:
#> X² = 65.742, df = 1, p = 0.000
#>
#> Fisher exact test:
#> Odds ratio = 17.393, p = 0.000
pand(scdf_est)
#> Percentage of all non-overlapping data
#>
#> Method: sort
#>
#> PAND = 79%
#> Φ = 0.44 ; Φ² = 0.194
#>
#> 200 measurements (50 Phase A, 150 Phase B) in 10 cases
#> Overlapping data: n = 42 ; percentage = 21
#>
#> 2 x 2 Matrix of percentages
#> A B total
#> A 14.5 10.5 25
#> B 10.5 64.5 75
#> total 25.0 75.0 100
#>
#> 2 x 2 Matrix of counts
#> A B total
#> A 29 21 50
#> B 21 129 150
#> total 50 150 200
#>
#>
#> Chi-Squared test:
#> X² = 38.720, df = 1, p = 0.000
#>
#> Fisher exact test:
#> Odds ratio = 8.360, p = 0.000
rand_test(scdf)
#> Randomization Test
#>
#> Combined test for 10 cases.
#>
#> Comparing phase 1 against phase 2
#> Statistic: Mean B-A
#>
#> Minimal length of each phase: A = 5 , B = 5
#> Observed statistic = 0.7679039
#>
#> Distribution based on a random sample of all 25937424601 possible combinations.
#> n = 500
#> M = 0.3085513
#> SD = 0.06906004
#> Min = 0.1427584
#> Max = 0.5118563
#>
#> Probability of an equal or higher value than the observed statistic:
#> p < 0.002
#>
#> Shapiro-Wilk Normality Test: W = 0.994; p = 0.037 (Hypothesis of normality rejected)
#>
#> Probabilty of observed statistic based on the assumption of normality:
#> z = 6.6515, p = 0.0000 (single sided)
rand_test(scdf_est)
#> Randomization Test
#>
#> Combined test for 10 cases.
#>
#> Comparing phase 1 against phase 2
#> Statistic: Mean B-A
#>
#> Minimal length of each phase: A = 5 , B = 5
#> Observed statistic = 0.7314301
#>
#> Distribution based on a random sample of all 25937424601 possible combinations.
#> n = 500
#> M = 0.269875
#> SD = 0.07922479
#> Min = 0.08001321
#> Max = 0.5456197
#>
#> Probability of an equal or higher value than the observed statistic:
#> p < 0.002
#>
#> Shapiro-Wilk Normality Test: W = 0.992; p = 0.013 (Hypothesis of normality rejected)
#>
#> Probabilty of observed statistic based on the assumption of normality:
#> z = 5.8259, p = 0.0000 (single sided)