PerFit (version 1.2)

cutoff: Compute a cutoff value given the scores of a person-fit statistic

Description

Compute a cutoff value given the scores of a person-fit statistic.

Usage

cutoff(x, method = "Quantile", Qlvl = 0.05, Blvl = 0.05, Breps = 1000, UDlvl = NA)

Arguments

x

Object of class "PerFit".

method

Method required to compute the cutoff score: "Quantile", "Bootstrap", "UserDefined". Default is "Quantile".

Qlvl

Quantile level (value between 0 and 1), only used when method="Quantile". Default is 0.05.

Blvl

Bootstrap level (value between 0 and 1), only used when method="Bootstrap". Default is 0.05.

Breps

Number of bootstrap resamples, only used when method="Bootstrap". Default is 1000.

UDlvl

User-defined level, only used when method="UserDefined".

Value

• A list with elements:
• cutoff
  Numeric. Value of the computed cutoff.
• prop.flagged
  Numeric. Proportion of respondents flagged (that is, with person-fit scores at or more extreme than the cutoff). It is equal to Qlvl when method="Quantile" and approximately equal to Blvl when method="Bootstrap".
• tail
  String with values "lower" or "upper". It indicates the type of person-fit statistic.

Details

This function computes a reference value (referred to as a 'cutoff') associated to the values of a person-fit statistic computed from a sample. The idea is to create a decision rule: Individual person-fit values at or more extreme than the cutoff result in flagging the corresponding respondents as (potentially) displaying aberrant response behavior. Depending on the person-fit statistic, an "extreme" score might be a very small (e.g., for Ht) or a very large (e.g., for G) value. The cutoff function routinely reports of which type the person-fit statistic being used is (tail="lower" or tail="upper", respectively). There are three methods available to estimate the cutoff value. When method="Quantile" the cutoff is the Qlvl (resp. 1-Qlvl) quantile of the sampling distribution for "lower" (resp. "upper") types of person-fit statistics. When method="Bootstrap" the cutoff is the median of the bootstrap distribution estimated by computing the Blvl (resp. 1-Blvl) quantile from each bootstrap resample (in a total of Breps) for "lower" (resp. "upper") types of person-fit statistics. Finally, the cutoff can be manually entered by the user (e.g., when it is available from prior data calibration) when method="UserDefined".

See Also

flagged.resp, plot.PerFit, PRFplot

Examples

# Load the inadequacy scale data (dichotomous item scores):
data(InadequacyData);

# As an example, compute the Ht person-fit scores:
Ht.PF <- Ht(InadequacyData);

# Compute the quantile-based 1% cutoff:
cutoff(Ht.PF,Qlvl=.01);