ident.ext {RSAtools}

Probe extrema in the response surface

Description

Identify reversal or acceleration points (generically called "extrema") in the LOC or LOIC of the response surface and test how many of them have outcome observations that significantly differ from what would be expected for predictor combinations on these points (that have the same level)

Usage

ident.ext(
  RSA_object,
  model = NULL,
  acceleration = c(0, 0),
  alpha = 0.05,
  z_tested = "observed",
  alphacorrection = "none",
  n_sample = NULL,
  verbose = TRUE,
  df_out = FALSE
)

Arguments

RSA_object

An RSA object

model

The model to be probed for extrema (reversal or acceleration points)

acceleration

Rates of accelerations along the LOC and LOIC to be inspected (0< abs(rate) < 1). Acceleration points will only appear if reversals do not exist, and if acceleration rates exist (if not, a warning will appear).

alpha

Alpha level for the one-sided confidence interval of the outcome predictions on the extrema

z_tested

Should significance tests be conducted on "observed" or "predicted" observation

alphacorrection

Set "Bonferroni" to adjust the alpha level for multiple testing when testing the outcome predictions of all data points behind the extrema

n_sample

Number of random draws to consider to find extrema. This option is used for large samples to increase speed in preliminary analyses, but it is not recommended for published results). Defaults to NULL.

verbose

Should extra information be printed?

df_out

Number of random draws to consider to find extrema. This option is used for large samples to increase speed in preliminary analyses, but it is not recommended for published results). Defaults to NULL.

Details

When testing for reversals or accelerations in nonlinear response surfaces involving quadratic or cubic polynomial families (FM4 to FM37), the RSAextrema function helps to determine the exact location of reversal or acceleration points along the lines of congruenc (LOC) or incongruence (LOIC), and the number and percentage of observations significantly affected by these reversals or accelerations (for a given probability level, alpha). This points are determined according to derivatives of the function according to rationales for combining polynomials (Núñez-Regueiro & Juhel, 2022, 2024).

Value

A table containing the location and percentages of observations above or below extrema

References

Núñez-Regueiro, F., Juhel, J. (2022). Model-Building Strategies in Response Surface Analysis Manuscript submitted for publication.

Núñez-Regueiro, F., Juhel, J. (2024). Response Surface Analysis for the Social Sciences II: Combinatory Rationales for Complex Polynomial Models Manuscript submitted for publication.

See Also

plotting.ext, RSAmodel