Package 'InteractionPoweR'

compute_adjustment

Description

Computes how much variable correlations need to be adjusted so that they have the desired correlation structure after transformation. Intended for internal use only.

Usage

compute_adjustment(
  r.x1.y,
  r.x2.y,
  r.x1x2.y,
  r.x1.x2,
  N.adjustment = 1e+06,
  tol = 0.005,
  iter = 10,
  k.x1,
  k.x2,
  k.y
)

Arguments

r.x1.y	Internal use only
r.x2.y	Internal use only
r.x1x2.y	Internal use only
r.x1.x2	Internal use only
N.adjustment	Internal use only
tol	Internal use only
iter	Internal use only
k.x1	Internal use only
k.x2	Internal use only
k.y	Internal use only

Value

Correlation adjustments.

Examples

compute_adjustment(r.x1.y = .2,r.x2.y = .2,r.x1x2.y = .1,r.x1.x2 = .2,
k.x1 = 0,k.x2=0,k.y=2)

---

See the correlation matrix for a 3-way interaction

Description

Prints or plots the correlation matrix for a 3-way interaction

Usage

cor.mat.3way(power.results, row.num = 1, return.plot = FALSE)

Arguments

power.results	Data frame of results from power_interaction_3way_r2().
row.num	Which row to show? Can only be a single number. Default is 1.
return.plot	Return a matrix (FALSE, default), or a plot (TRUE)?

Value

A matrix or a ggplot2 object

Examples

power_analysis = power_interaction_3way_r2(detailed_results = TRUE,N = c(1000),
r.x1.y = .2,r.x2.y = .3,r.x3.y = .1,r.x1x2.y = .01,r.x1x3.y = .05,r.x2x3.y = .1,
b.x1x2x3 = 0.1,r.x1.x2 = .1,r.x1.x3 = .1,r.x2.x3 = .1,
rel.x1 = 1,rel.x2 = 1,rel.x3 = 1,rel.y = 1 )
cor.mat.3way(power_analysis)

---

Generate interaction data set

Description

Simulate a single data set with an interaction (y ~ x1 + x2 + x1*x2). All values other than 'N' are population-level effects - the values within any single simulated data set will vary around the defined values.

Usage

generate_interaction(
  N,
  r.x1.y,
  r.x2.y,
  r.x1x2.y,
  r.x1.x2,
  rel.x1 = 1,
  rel.x2 = 1,
  rel.y = 1,
  k.x1 = 0,
  k.x2 = 0,
  k.y = 0,
  adjust.correlations = TRUE,
  tol = 0.005,
  iter = 10,
  N.adjustment = 1e+06,
  r.x1.y.adjust = NULL,
  r.x2.y.adjust = NULL,
  r.x1.x2.adjust = NULL,
  r.x1x2.y.adjust = NULL,
  internal.adjust = FALSE,
  skew.x1 = NA,
  skew.x2 = NA,
  skew.y = NA
)

Arguments

N	Sample size. Must be a positive integer. Has no default value.
r.x1.y	Pearson's correlation between x1 and y. Must be between -1 and 1. Has no default value.
r.x2.y	Pearson's correlation between x2 and y. Must be between -1 and 1. Assumed to be the 'moderator' in some functions. Has no default value.
r.x1x2.y	Pearson's correlation between the interaction term x1x2 (x1 * x2) and y. Must be between -1 and 1. Has no default value.
r.x1.x2	Pearson's correlation between x1 and x2. Must be between -1 and 1. Has no default value.
rel.x1	Reliability of x1 (e.g. test-retest reliability, ICC, Cronbach's alpha). Default is 1 (perfect reliability). Must be greater than 0 and less than or equal to 1.
rel.x2	Reliability of x2 (e.g. test-retest reliability, ICC, Cronbach's alpha). Default is 1 (perfect reliability). Must be greater than 0 and less than or equal to 1.
rel.y	Reliability of xy (e.g. test-retest reliability, ICC, Cronbach's alpha). Default is 1 (perfect reliability). Must be greater than 0 and less than or equal to 1.
k.x1	Number of discrete values for x1. Can be used to make a variable binary or ordinal.
k.x2	Number of discrete values for x2. Can be used to make a variable binary or ordinal.
k.y	Number of discrete values for y.Can be used to make a variable binary or ordinal.
adjust.correlations	If variables are ordinal or binary, should correlations be adjusted so that output data has the specified correlation structure? Default is TRUE.
tol	Correlation adjustment tolerance. When adjust.correlations = TRUE, correlations are adjusted so that the population correlation is within r='tol' of the target. Default = 0.005.
iter	Max number of iterations to run the correlation adjustment for. Typically only a couple are needed. Default = 10.
N.adjustment	Sample size to use when adjusting correlations. Default = 1000000.
r.x1.y.adjust	Internal use only.
r.x2.y.adjust	Internal use only.
r.x1.x2.adjust	Internal use only.
r.x1x2.y.adjust	Internal use only.
internal.adjust	Internal use only.
skew.x1	No longer supported.
skew.x2	No longer supported.
skew.y	No longer supported.

Value

A data frame containing variables 'x1', 'x2', 'y', and 'x1x2'. 'x1x2' is x1*x2. The correlations between these variables are drawn from the defined population-level values. Output variables are all z-scored (mean=0, sd=1).

Examples

dataset <- generate_interaction(N = 10,r.x1.y = 0,r.x2.y = .1,r.x1x2.y = -.2,r.x1.x2 = .3)

---

Creates the input to power_interaction_r2_covs()

Description

Companion function to 'power_interaction_r2_covs()'. Generates a formatted list for users to specify the analysis parameters.

Usage

generate.interaction.cov.input(c.num)

Arguments

c.num

Number of covariates in the model.

Value

A list to be used with the 'power_interaction_r2_covs()' function.

Examples

ex1 = generate.interaction.cov.input(c.num=2)
ex1$correlations$r.y.x1x2 = c(0.1,0.2,0.3)

---

Name key for plotting

Description

Expanded variable names so that plots look nicer.

Usage

data(name_key)

Format

A data frame with 25 rows and 2 variables

---

norm2ordinal

Description

Transforms a vector with a normal distribution to a binomial distribution with two values.

Usage

norm2ordinal(x, k)

Arguments

x	Input vector
k	Number of discrete values (e.g., 2=binary, 5=likert scale)

Value

A ordinal or binary variable

Examples

norm2ordinal(x = rnorm(n = 100,mean = 0,sd = 1),k=2)

---

Plot interaction

Description

Plots a single simulated interaction data set

Usage

plot_interaction(data, q = 3)

Arguments

data	Output of generate_interaction().
q	Simple slope quantiles. Default is 2. X2 is the default moderator, unless X1 is already binary. Must be a positive integer > 1.

Value

A ggplot2 object

Examples

dataset <- generate_interaction(N = 250,r.x1.y = 0,r.x2.y = .1,r.x1x2.y = -.2,r.x1.x2 = .3)
plot_interaction(dataset,q=3)

---

Plot power curve

Description

Plot the output of power_interaction().

Usage

plot_power_curve(
  power_data,
  x = NULL,
  group = NULL,
  facets = NULL,
  power_target = 0.8
)

Arguments

power_data	Data frame of results from power_interaction(). Can accept the raw results if up to 3 parameters were varied during simulation. Any more and data should be filtered first.
x	Optional, the x-axis of the plot. Default is the first variable after 'pwr'.
group	Optional, grouping variable for the line color. Default is the second variable after 'pwr', if present.
facets	Optional, grouping variable for plot facets. Default is the third variable after 'pwr' if present.
power_target	The target power. Default is 80%.

Value

A ggplot2 object

Examples

power_analysis <- power_interaction(n.iter = 10,N = seq(100,300,by=100),
 r.x1.y = 0,r.x2.y = .1,r.x1x2.y = -.2,r.x1.x2 = .3,detailed_results = TRUE)
 plot_power_curve(power_analysis)

---

Simple slope plot

Description

Plots the simple slope min and max estimates from power_interaction().

Usage

plot_simple_slope(power_data, x = NULL, facets = NULL)

Arguments

power_data	Data frame of results from power_interaction(). Can accept the raw results if up to 2 parameters were varied during simulation. Any more and data should be filtered first.
x	Optional, the x-axis of the plot. Default is the first variable after 'pwr'.
facets	Optional, grouping variable for plot facets. Default is the second variable after 'pwr' if present.

Value

A ggplot2 object

Examples

power_analysis <- power_interaction(n.iter = 10,N = seq(100,300,by=100),
r.x1.y = 0,r.x2.y = .1,r.x1x2.y = -.2,r.x1.x2 = .3,detailed_results = TRUE)
plot_simple_slope(power_analysis)

---

Power estimate

Description

Uses regression to estimate the value needed to attain the target power, given a set of simulation results.

Usage

power_estimate(power_data, x, power_target)

Arguments

power_data	Output of power_interaction().
x	The name of the target variable as a character string.
power_target	The desired power level. Must be between 0 and 1 (e.g., 0.8 for 80% power).

Value

A data frame containing the value of x that achieves the target power for each combination of settings. Will return NA if target power is outside the simulation data.

Examples

simulation_results = power_interaction_r2(N=seq(100,300,by=10),
r.x1.y=0.2, r.x2.y=.2,r.x1x2.y=0.2,r.x1.x2=.2)
power_estimate(power_data = simulation_results, x = "N", power_target = .8)

---

Power analysis for interactions

Description

Power analysis for interaction models, by simulation. A set of n.iter simulations is run for each unique combination of model settings.

Usage

power_interaction(
  n.iter,
  N,
  r.x1.y,
  r.x2.y,
  r.x1x2.y,
  r.x1.x2,
  rel.x1 = 1,
  rel.x2 = 1,
  rel.y = 1,
  k.x1 = 0,
  k.x2 = 0,
  k.y = 0,
  adjust.correlations = TRUE,
  alpha = 0.05,
  q = 2,
  cl = NULL,
  ss.IQR = 1.5,
  N.adjustment = 1e+06,
  detailed_results = FALSE,
  full_simulation = FALSE,
  tol = 0.005,
  iter = 10,
  skew.x1 = NA,
  skew.x2 = NA,
  skew.y = NA
)

Arguments

n.iter	Number of iterations. The number of simulations to run for each unique setting combination. Must be a positive integer.
N	Sample size. Must be a positive integer. Has no default value. Can be a single value or a vector of values.
r.x1.y	Pearson's correlation between x1 and y. Must be between -1 and 1.. Has no default value. Can be a single value or a vector of values.
r.x2.y	Pearson's correlation between x2 and y. Must be between -1 and 1.. Assumed to be the 'moderator' in some functions. Has no default value. Can be a single value or a vector of values.
r.x1x2.y	Pearson's correlation between the interaction term x1x2 (x1 * x2) and y. Must be between -1 and 1.. Has no default value. Can be a single value or a vector of values.
r.x1.x2	Pearson's correlation between x1 and x2. Must be between -1 and 1.. Has no default value. Can be a single value or a vector of values.
rel.x1	Reliability of x1 (e.g. test-retest reliability, ICC, Cronbach's alpha). Default is 1 (perfect reliability). Must be greater than 0 and less than or equal to 1.
rel.x2	Reliability of x2 (e.g. test-retest reliability, ICC, Cronbach's alpha). Default is 1 (perfect reliability). Must be greater than 0 and less than or equal to 1.
rel.y	Reliability of xy (e.g. test-retest reliability, ICC, Cronbach's alpha). Default is 1 (perfect reliability). Must be greater than 0 and less than or equal to 1.
k.x1	Number of discrete values for x1. Can be used to make a variable binary or ordinal.
k.x2	Number of discrete values for x2. Can be used to make a variable binary or ordinal.
k.y	Number of discrete values for y. Can be used to make a variable binary or ordinal.
adjust.correlations	If variables are ordinal or binary, should correlations be adjusted so that output data has the specified correlation structure? Default is TRUE.
alpha	The alpha. At what p-value is the interaction deemed significant? Default is 0.05.
q	Simple slopes. How many quantiles should x2 be split into for simple slope testing? Default is 2. Simple slope testing returns the effect-size (slope) of y~x1 for the two most extreme quantiles of x2. If q=3 then the two slopes are y~x1 for the bottom 33% of x2, and the top 33% of x2.
cl	Number of clusters to use for running simulations in parallel (recommended). Default is 1 (i.e. not in parallel).
ss.IQR	Simple slope IQR. Multiplier when estimating the distribution of simple slopes within each simulation setting. Default is 1.5.
N.adjustment	Sample size for simulations where correlation matrix is corrected to allow for binary/ordinal variables. Default is 1000000
detailed_results	Default is FALSE. Should detailed results be reported?
full_simulation	Default is FALSE. If TRUE, will return a list that includes the full per-simulation results.
tol	Correlation adjustment tolerance. When adjust.correlations = TRUE, correlations are adjusted so that the population correlation is within r='tol' of the target. Default = 0.005.
iter	Max number of iterations to run the correlation adjustment for. Typically only a couple are needed. Default = 10.
skew.x1	No longer supported.
skew.x2	No longer supported.
skew.y	No longer supported.

Value

A data frame containing the power (% significant results) for each unique setting combination. If full_simulation = TRUE will return a list, with one data frame that includes power, and a second that includes raw simulation results.

Examples

power_interaction(n.iter=10, N=10,r.x1.y=0.2, r.x2.y=.2,r.x1x2.y=0.5,r.x1.x2=.2)

---

Analytic power analysis for 3-way interactions

Description

Power analysis for 3-way interaction models, computed via change in R2. Valid for interactions with continuous, normally distributed, variables. Either b.x1x2x3 or f2 can be used to specify the magnitude of the interaction effect size.

Usage

power_interaction_3way_r2(
  N,
  b.x1x2x3,
  r.x1.y,
  r.x2.y,
  r.x3.y,
  r.x1x2.y,
  r.x1x3.y,
  r.x2x3.y,
  r.x1.x2,
  r.x1.x3,
  r.x2.x3,
  rel.x1 = 1,
  rel.x2 = 1,
  rel.x3 = 1,
  rel.y = 1,
  alpha = 0.05,
  detailed_results = FALSE,
  cl = NULL
)

Arguments

N	Sample size. Must be a positive integer. Has no default value. Can be a single value or a vector of values.
b.x1x2x3	Regression coefficient of the 3-way interaction term x1x2x3. Should not be specified if f2 is specified. Must be between -1 and 1. Default is NULL. Can be a single value or a vector of values.
r.x1.y	Pearson's correlation between x1 and y. Must be between -1 and 1. Has no default value. Can be a single value or a vector of values.
r.x2.y	Pearson's correlation between x2 and y. Must be between -1 and 1. Assumed to be the 'moderator' in some functions. Has no default value. Can be a single value or a vector of values.
r.x3.y	Pearson's correlation between x3 and y. Must be between -1 and 1. Assumed to be the 'moderator' in some functions. Has no default value. Can be a single value or a vector of values.
r.x1x2.y	Pearson's correlation between the interaction term x1x2 (x1 * x2) and y. Must be between -1 and 1. Has no default value. Can be a single value or a vector of values.
r.x1x3.y	Pearson's correlation between the interaction term x1x2 (x1 * x3) and y. Must be between -1 and 1. Has no default value. Can be a single value or a vector of values.
r.x2x3.y	Pearson's correlation between the interaction term x1x2 (x2 * x3) and y. Must be between -1 and 1. Has no default value. Can be a single value or a vector of values.
r.x1.x2	Pearson's correlation between x1 and x2. Must be between -1 and 1. Has no default value. Can be a single value or a vector of values.
r.x1.x3	Pearson's correlation between x1 and x3. Must be between -1 and 1. Has no default value. Can be a single value or a vector of values.
r.x2.x3	Pearson's correlation between x2 and x3. Must be between -1 and 1. Has no default value. Can be a single value or a vector of values.
rel.x1	Reliability of x1 (e.g. test-retest reliability, ICC, Cronbach's alpha). Default is 1 (perfect reliability). Must be greater than 0 and less than or equal to 1.
rel.x2	Reliability of x2 (e.g. test-retest reliability, ICC, Cronbach's alpha). Default is 1 (perfect reliability). Must be greater than 0 and less than or equal to 1.
rel.x3	Reliability of x3 (e.g. test-retest reliability, ICC, Cronbach's alpha). Default is 1 (perfect reliability). Must be greater than 0 and less than or equal to 1.
rel.y	Reliability of xy (e.g. test-retest reliability, ICC, Cronbach's alpha). Default is 1 (perfect reliability). Must be greater than 0 and less than or equal to 1.
alpha	The alpha. At what p-value is the interaction deemed significant? Default is 0.05.
detailed_results	Default is FALSE. Should detailed results be reported? Returns regression slopes, f2, r2, and the full correlation matrix.
cl	Number of clusters to use for running simulations in parallel. Default is NULL (i.e. not in parallel). Useful when running several thousand analyses at once.

Value

A data frame containing the power for each unique setting combination.

Examples

power_interaction_3way_r2(N=1000,r.x1.y = .1,r.x2.y = .2,r.x3.y = .3,
r.x1x2.y =  .05,r.x1x3.y =  .07,r.x2x3.y =  .09,b.x1x2x3 =0.01,
r.x1.x2 = .2,r.x1.x3 = .4,r.x2.x3 = .3)

---

Analytic power analysis for interactions

Description

Power analysis for interaction models, computed via change in R2. Valid for interactions with continuous, normally distributed, variables.

Usage

power_interaction_r2(
  N,
  r.x1.y,
  r.x2.y,
  r.x1x2.y,
  r.x1.x2,
  rel.x1 = 1,
  rel.x2 = 1,
  rel.y = 1,
  alpha = 0.05,
  detailed_results = FALSE
)

Arguments

N	Sample size. Must be a positive integer. Has no default value. Can be a single value or a vector of values.
r.x1.y	Pearson's correlation between x1 and y. Must be between -1 and 1. Has no default value. Can be a single value or a vector of values.
r.x2.y	Pearson's correlation between x2 and y. Must be between -1 and 1. Assumed to be the 'moderator' in some functions. Has no default value. Can be a single value or a vector of values.
r.x1x2.y	Pearson's correlation between the interaction term x1x2 (x1 * x2) and y. Must be between -1 and 1. Has no default value. Can be a single value or a vector of values.
r.x1.x2	Pearson's correlation between x1 and x2. Must be between -1 and 1. Has no default value. Can be a single value or a vector of values.
rel.x1	Reliability of x1 (e.g. test-retest reliability, ICC, Cronbach's alpha). Default is 1 (perfect reliability). Must be greater than 0 and less than or equal to 1.
rel.x2	Reliability of x2 (e.g. test-retest reliability, ICC, Cronbach's alpha). Default is 1 (perfect reliability). Must be greater than 0 and less than or equal to 1.
rel.y	Reliability of xy (e.g. test-retest reliability, ICC, Cronbach's alpha). Default is 1 (perfect reliability). Must be greater than 0 and less than or equal to 1.
alpha	The alpha. At what p-value is the interaction deemed significant? Default is 0.05.
detailed_results	Default is FALSE. Should detailed results be reported?

Value

A data frame containing the power for each unique setting combination.

Examples

power_interaction_r2(N=seq(100,300,by=10),r.x1.y=0.2, r.x2.y=.2,r.x1x2.y=0.2,r.x1.x2=.2)

---

Analytic interaction power analysis with covariates

Description

Analytic power analysis of an interaction model with covariates. Additional covariate x main effect interaction terms are additionally added.

Usage

power_interaction_r2_covs(
  cov.input,
  N,
  alpha = 0.05,
  detailed_results = FALSE,
  cl = NULL
)

Arguments

cov.input	Output of 'power_interaction_r2_covs()'. Variable correlations and reliabilities are set by first modifying this list.
N	Sample size. Must be a positive integer. Has no default value. Can be a single value or a vector of values.
alpha	The alpha. At what p-value is the interaction deemed significant? Default is 0.05.
detailed_results	Default is FALSE. Should detailed results be reported?
cl	Number of clusters to use for running simulations in parallel. Default is NULL (i.e. not in parallel). Useful when running several thousand analyses at once.

Value

A data frame containing the analytic power for each unique setting combination.

Examples

ex1 = generate.interaction.cov.input(c.num=2)
ex1$correlations$r.y.x1x2 = c(0.1,0.2,0.3)
power_interaction_r2_covs(cov.input = ex1,N=100)

---

See the simple slopes for a 3-way interaction

Description

Prints or plots the simple slopes for a 3-way interaction

Usage

simple.slopes.3way(power.results, row.num = 1, return.plot = FALSE)

Arguments

power.results	Data frame of results from power_interaction_3way_r2().
row.num	Which row to show? Can only be a single number. Default is 1.
return.plot	Return a matrix (FALSE, default), or a plot (TRUE)?

Value

A matrix or a ggplot2 object

Examples

power_analysis = power_interaction_3way_r2(detailed_results = TRUE,N = c(1000),
r.x1.y = .2,r.x2.y = .3,r.x3.y = .1,r.x1x2.y = .01,r.x1x3.y = .05,r.x2x3.y = .1,
b.x1x2x3 = 0.1,r.x1.x2 = .1,r.x1.x3 = .1,r.x2.x3 = .1,
rel.x1 = 1,rel.x2 = 1,rel.x3 = 1,rel.y = 1 )
simple.slopes.3way(power_analysis)

---

Test interaction

Description

Test the interaction from a single simulated data set.

Usage

test_interaction(
  data,
  alpha = 0.05,
  detailed_results = FALSE,
  q = 2,
  simple = FALSE
)

Arguments

data	Simulated data set. Output of 'generate_interaction()'.
alpha	The alpha. At what p-value is the interaction deemed significant? Default is 0.05.
detailed_results	Should results beyond the linear model (change in R2, simple slopes, correlations, and confidence intervals) be returned? Default is FALSE.
q	Simple slopes. How many quantiles should x2 be split into for simple slope testing? Default is 2. Simple slope testing returns the effect-size (slope) of y~x1 for the two most extreme quantiles of x2. If q=3 then the two slopes are y~x1 for the bottom 33% of x2, and the top 33% of x2.
simple	For internal use. Default is FALSE.

Value

Either a named list or a data frame containing the results of the regression y~x1+x2+x1*x2, the pearson's correlation between y, x1,x2, and x1x2, and the slopes of the simple slopes.

Examples

dataset <- generate_interaction(N = 250,r.x1.y = 0,r.x2.y = .1,r.x1x2.y = -.2,r.x1.x2 = .3)
test_interaction(data = dataset, alpha=0.05, q=2)

---