dynConfiR (version 0.0.4)

PDFtoQuantiles: Get Quantiles from vectors of PDF or CDF values

Description

CDFtoQuantiles computes quantiles for a given CDF. PDFtoQuantiles computes the quantiles for given PDF values within groups of other variables, if available.

Usage

PDFtoQuantiles(pdf_df, p = c(0.1, 0.3, 0.5, 0.7, 0.9), agg_over = NULL,
  scaled = FALSE)
CDFtoQuantiles(cdf, x = NULL, p)

Value

PDFtoQuantiles returns a tibble with columns p and q indicating probabilities and respective quantiles. Furthermore, the output has grouping columns identical to the additional columns in the input (without rt/x, dens and densscaled), but without the ones in the agg_over argument. CDFtoQuantiles

returns only a data.frame with columns p and q.

Arguments

pdf_df

dataframe. Should have at least two columns:

• rt (for reaction times) or x for the support values of the pdf

• dens or pdf for the pdf values

• All other columns will be used as grouping factors, for which separate quantiles will be returned.

p

numeric vector. Probabilities for returned quantiles. Default: c(.1, .3, .5, .7, .9).

agg_over

character. Names of columns in pdf_df to aggregate over (using the mean of densities, which is valid only, if groups occur with equal probabilities) before computing the quantiles.

scaled

logical. Indicating whether the pdf values are from a proper probability distribution. Non-scaled pdfs will scaled to 1. If scaled is TRUE, this may cause problems with high probabilities. In any case we strongly recommend to cover the most probability mass with the values in the support vector.

cdf

numeric. A increasing vector of the same length as x giving the CDF for respective x-Values. Dataframe inputs are accepted. If a column x is available there, this will be used as support values.

x

numeric. A increasing vector of same length as cdf. Can also be specified as column of cdf.

Author

Sebastian Hellmann.

Details

For a reasonable accuracy the number of steps in the support column (rt/x) should be high, i.e. the distance between values small. We recommend, to ensure that the support vector in the input to be equidistant, i.e. the difference between consecutive support values should be constant, though this is not required. If both column names x and rt are present in pdf_df, rt will be preferred. Attention should be given to the columns of pdf_df other than rt/x and dens/pdf.

The column for the pdf may be scaled to integrate to 1 but do not have to.

Quantile computation in the dynConfiR package

As argument pdf_df, the outputs of predictRT and predictRTModels from the dynConfiR package can be used. In the context of confidence models grouping factors often used are conditions, correct/incorrect answers and confidence ratings.

Examples

## Demonstrate PDFtoQuantiles
pred <- expand.grid(model = c("dynWEV", "PCRMt"),
                    rt =  seq(0, 15, length.out=1200),
                    condition = c(1,2,3),
                    rating = c(1,2))
pred$dens <- dchisq(pred$rt, 3) # pdf may also be used as column name
head(pred)
res <- PDFtoQuantiles(pred, p=c(0.3, 0.5, 0.7))
head(res)
nrow(res) #= 3(quantiles)*2(models)*3(conditions)*2(rating)
# Compare to true quantiles of Chi-square distribution
qchisq(p=c(0.3, 0.5, 0.7), 3)
res$q[1:3]


res2 <- PDFtoQuantiles(pred, p=c(0.3, 0.5, 0.7), agg_over = "model")
nrow(res2) #=18 because res aggregated over models

# \donttest{
  pred$pdf <- dchisq(pred$rt, 3)
  head(pred)
  # following call throws a warning, because both columns pdf and dens are present
  PDFtoQuantiles(pred, p=c(0.3, 0.5, 0.7), agg_over = "model")
# }

# \donttest{
  pred2 <- data.frame(rt=seq(0, 7, length.out=100))
  pred2$dens <- dchisq(pred2$rt, 5)
  # following call throws a warning, because density is assumed to be scaled (scaled=TRUE), i.e.
  # integrate to 1, but the .95 quantile is not reached in the rt column
  PDFtoQuantiles(pred2, p=c(0.3, 0.5, 0.95), scaled=TRUE) # Gives a warning
# }

## Demonstrate CDFtoQuantiles
X <- seq(-2, 2, length.out=300)
pdf_values <- pnorm(X)
CDFtoQuantiles(pdf_values, X, p=c(0.2, 0.5, 0.8))
qnorm(c(0.2, 0.5, 0.8))