RSA: Performs several RSA model tests on a data set with two...

In RSA: Response Surface Analysis

Performs several RSA model tests on a data set with two predictors

Description

Performs several RSA model tests on a data set with two predictors

Usage

RSA(
  formula,
  data = NULL,
  center = "none",
  scale = "none",
  na.rm = FALSE,
  out.rm = TRUE,
  breakline = FALSE,
  models = "default",
  cubic = FALSE,
  verbose = TRUE,
  add = "",
  estimator = "MLR",
  se = "robust",
  missing = NA,
  control.variables = c(),
  center.control.variables = FALSE,
  ...
)

Arguments

formula	A formula in the form z ~ x*y, specifying the variable names used from the data frame, where z is the name of the response variable, and x and y are the names of the predictor variables.
data	A data frame with the variables
center	Method for centering the predictor variables before the analysis. Default option ("none") applies no centering. "pooled" centers the predictor variables on their pooled sample mean, which preserves the commensurability of the predictor scales. "variablewise" centers the predictor variables on their respective sample mean. You should think carefully before applying the "variablewise" option, as centering the predictor variables at different values (e.g., their respective means) can affect the commensurability of the predictor scales.
scale	Method for scaling the predictor variables before the analysis. Default option ("none") applies no scaling. "pooled" scales the predictor variables on their pooled sample SD, which preserves the commensurability of the predictor scales. "variablewise" scales the predictor variables on their respective sample SD. You should think carefully before applying the "variablewise" option, as scaling the predictor variables at different values (e.g., their respective SDs) can affect the commensurability of the predictor scales.
na.rm	Remove missings before proceeding?
out.rm	Should outliers according to Bollen & Jackman (1980) criteria be excluded from the analyses? In large data sets this analysis is the speed bottleneck. If you are sure that no outliers exist, set this option to FALSE for speed improvements.
breakline	Should the breakline in the unconstrained absolute difference model be allowed (the breakline is possible from the model formulation, but empirically rather unrealistic ...). Defaults to FALSE
models	A vector with names of all models that should be computed. Should be any from c("absdiff", "absunc", "diff", "mean", "additive", "IA", "SQD", "RR", "SRR", "SRRR", "SSQD", "SRSQD", "full", "null", "onlyx", "onlyy", "onlyx2", "onlyy2", "cubic", "CA", "RRCA", "CL", "RRCL"). For models="all", all models are computed, for models="default" all models besides absolute difference models are computed.
cubic	Should the cubic models with the additional terms Y^3, XY^2, YX^2, and X^3 be included?
verbose	Should additional information during the computation process be printed?
add	Additional syntax that is added to the lavaan model. Can contain, for example, additional constraints, like "p01 == 0; p11 == 0"
estimator	Type of estimator that should be used by lavaan. Defaults to "MLR", which provides robust standard errors, a robust scaled test statistic, and can handle missing values. If you want to reproduce standard OLS estimates, use estimator="ML" and se="standard"
se	Type of standard errors. This parameter gets passed through to the sem function of the lavaan package. See options there. By default, robust SEs are computed. If you use se="boot", lavaan provides CIs and p-values based on the bootstrapped standard error. If you use confint(..., method="boot"), in contrast, you get CIs and p-values based on percentile bootstrap (see also confint.RSA).
missing	Handling of missing values (this parameter is passed to the lavaan sem function). By default (missing=NA), Full Information Maximum Likelihood (FIML) is employed in case of missing values. If cases with missing values should be excluded, use missing = "listwise".
control.variables	A string vector with variable names from data. These variables are added as linear predictors to the model (in order "to control for them"). No interactions with the other variables are modeled.
center.control.variables	Should the control variables be centered before analyses? This can improve interpretability of the intercept, which will then reflect the predicted outcome value at the point (X,Y)=(0,0) when all control variables take their respective average values.
...	Additional parameters passed to the lavaan sem function.

Details

Even if the main variables of the model are normally distributed, their squared terms and interaction terms are necessarily non-normal. By default, the RSA function uses a scaled test statistic (test="Satorra-Bentler") and robust standard errors (se="robust"), which are robust against violations of the normality assumption.

Why does my standard polynomial regression give different p-values and SEs than the RSA package? Shouldn't they be the same? This is due to the robust standard errors employed in the RSA package. If you set estimator="ML" and se="standard", you get p-values that are very close to the standard approach. (They might still not be identical because the standard regression approach usually uses an OLS estimator and RSA uses an ML estimator).

Experimental feature (use with caution!): You can also fit binary outcome variables with a probit link function. For that purpose, the response variable has to be defined as "ordered", and the lavaan estimator changed to "WLSMV": r1.binary <- RSA(z.binary~x*y, df, ordered="z.binary", estimator="WLSMV", model="full") (for more details see the help file of the sem function in the lavaan package.). The results can also be plotted with probabilities on the z axis using the probit link function: plot(r1.binary, link="probit", zlim=c(0, 1), zlab="Probability"). For plotting, the binary outcome variable must be coded with 0 and 1 (not as a factor). lavaan at the moment only supports a probit link function for binary outcomes, not a logit link. Please be aware that this experimental feature can fit the full model, but most other functions (such as model comparisons) might break and errors might show up.

Note

For explanations of the meaning of the various different models that can be estimated, please see Schönbrodt (2016) for the second-order models (i.e., all models but "CA", "RRCA", "CL", "RRCL") and Humberg et al. (in press) for the third-order (cubic) models ("CA", "RRCA", "CL", "RRCL").

For most of the second-order models, several auxiliary parameters are computed from the estimated model coefficients (e.g., a1, ..., a5, p10, p11, p20, p21) and printed in the summary output. They can be used to guide interpretation by means of response surface methodology. Some references that explain how to use these parameters for interpretation are Edwards (2002; comprehensive overview of response surface methodology), Humberg et al. (2019; interpretation of a1, a2, a3, a4, p10, and p11, and how to use them to investigate congruence effects), Nestler et al. (2019; interpretation of a1, a2, a3, a4, and a5, and how to use them to investigate congruence effects, see in particular Appendix A for the introduction of a5), and Schönbrodt et al. (2018; interpretation of a1, ..., a5, see in particular Appendix A for a5).

The print function provides descriptive statistics about discrepancies in the predictors (with respect to numerical congruence). A cutpoint of |delta z| > 0.5 is used. The computation generally follows the idea of Shannock et al (2010) and Fleenor et al. (1996). However, in contrast to them, we standardize to the common mean and the common SD of both predictor variables. Otherwise we would break commensurability, and a person who has x=y in the unstandardized variable could become incongruent after variable-wise standardization. See also our discussion of commensurability and scale transformation in the cubic RSA paper (Humberg et al., in press; see pp. 35 - 37 in the preprint at https://psyarxiv.com/v6m35).

References

Edwards, J. R. (2002). Alternatives to difference scores: Polynomial regression analysis and response surface methodology. In F. Drasgow & N. W. Schmitt (Eds.), Advances in measurement and data analysis (pp. 350–400). San Francisco, CA: Jossey-Bass.

Humberg, S., Nestler, S., & Back, M. D. (2019). Response Surface Analysis in Personality and Social Psychology: Checklist and Clarifications for the Case of Congruence Hypotheses. Social Psychological and Personality Science, 10(3), 409–419. doi:10.1177/1948550618757600

Humberg, S., Schönbrodt, F. D., Back, M. D., & Nestler, S. (in press). Cubic response surface analysis: Investigating asymmetric and level-dependent congruence effects with third-order polynomial models. Psychological Methods. doi:10.1037/met0000352

Nestler, S., Humberg, S., & Schönbrodt, F. D. (2019). Response surface analysis with multilevel data: Illustration for the case of congruence hypotheses. Psychological Methods, 24(3), 291–308. doi:10.1037/met0000199

Schönbrodt, F. D. (2016). Testing fit patterns with polynomial regression models. Retrieved from osf.io/3889z

Schönbrodt, F. D., Humberg, S., & Nestler, S. (2018). Testing similarity effects with dyadic response surface analysis. European Journal of Personality, 32(6), 627-641. doi:10.1002/per.2169

See Also

demoRSA, plotRSA, RSA.ST, confint.RSA, compare

Examples

# Compute response surface from a fake data set
set.seed(0xBEEF)
n <- 300
err <- 15
x <- rnorm(n, 0, 5)
y <- rnorm(n, 0, 5)
df <- data.frame(x, y)
df <- within(df, {
	diff <- x-y
	absdiff <- abs(x-y)
	SD <- (x-y)^2
	z.diff <- diff + rnorm(n, 0, err)
	z.abs <- absdiff + rnorm(n, 0, err)
	z.sq <- SD + rnorm(n, 0, err)
	z.add <- diff + 0.4*x + rnorm(n, 0, err)
	z.complex <- 0.4*x + - 0.2*x*y + + 0.1*x^2 - 0.03*y^2 + rnorm(n, 0, err)
})
df$z.binary <- as.numeric(df$z.sq < median(df$z.sq))

## Not run: 
r1 <- RSA(z.sq~x*y, df)
summary(r1)
compare(r1)
plot(r1)
plot(r1, model="SRSQD")
plot(r1, model="full", type="c")
getPar(r1, "coef")	# print model parameters including SE and CI
RSA.ST(r1)	# get surface parameters

# Example with binary outcome 
(probit regression, see Details; Experimental and a dirty workaround!).
# The standard summary output does not work; you have to access the full model directly:
r1.binary <- RSA(z.binary~x*y, df, ordered="z.binary", estimator="WLSMV", 
    model="full", se="standard")
# --> ignore the warning
summary(r1.binary$models[["full"]])
plot(r1.binary, link="probit", zlim=c(0, 1), zlab="Probability")

# Motive congruency example
data(motcon)
r.m <- RSA(postVA~ePow*iPow, motcon)

# Get boostrapped CIs with 10 bootstrap samples (usually this should be set to 5000 or higher),
# only from the SSQD model
c1 <- confint(r.m, model="SSQD", method="boot", R=10)

# Plot the final model
plot(r.m, model="RR", xlab="Explicit power motive", 
		ylab="Implicit power motive", zlab="Affective valence")
		
# Inclusion of control variables: Fake data on self-other agreement
data(selfother)
r.c <- RSA(liking~IQ_self*IQ_friend, 
           center="pooled",
           control.variables=c("age", "int"),
           center.control.variables = TRUE,
           data=selfother)
summary(r.c)	
		

## End(Not run)

RSA documentation built on Jan. 12, 2023, 9:07 a.m.