bfactor_log_interpret {pcal}

Interpretation of the logarithms of Bayes factors

Description

Quantify the strength of the evidence provided by the data to a model/hypothesis according to the Bayes factor interpretation scale suggested by Jeffreys (1961).

Usage

bfactor_log_interpret(bf, base = exp(1))

Arguments

bf

A numeric vector.

base

A numeric vector of length one. Must be a positive number.

Details

Bayes factors are a summary of the evidence provided by the data to a model/hypothesis, and are often reported on a logarithmic scale. Jeffreys (1961) suggested the interpretation of Bayes factors in half-units on the base 10 logarithmic scale, as indicated in the following table:

log10(Bayes factor)	Bayes factor	Evidence
[-Inf, 0[	[0, 1[	Negative
[0, 0.5[	[1, 3.2[	Weak
[0.5, 1[	[3.2, 10[	Substantial
[1, 1.5[	[10, 32[	Strong
[1.5, 2[	[32, 100[	Very Strong
[2, +Inf[	[100, +Inf[	Decisive

bfactor_log_interpret takes (base base) logarithms of Bayes factors as input and returns the strength of the evidence provided by the data in favor of the model/hypothesis in the numerator of the Bayes factors (usually the null hypothesis) according to the according to the aforementioned table.

When comparing results with those from standard likelihood ratio tests, it is convenient to put the null hypothesis in the denominator of the Bayes factor so that bfactor_log_interpret returns the strength of the evidence against the null hypothesis. If bf was obtained with the null hypothesis on the numerator, one can use bfactor_log_interpret(1/bf) to obtain the strength of the evidence against the null hypothesis.

Value

Returns a character vector with the same length as bf.

References

Jeffreys H (1961). Theory of probability, Oxford Classic Texts In The Physical Sciences, 3 edition. Oxford University Press.

See Also

• bfactor_log_interpret_kr for an alternative interpretation scale.

• bfactor_interpret and bfactor_interpret_kr for the interpretation of Bayes factors in levels.

• bfactor_to_prob to turn Bayes factors into posterior probabilities.

• bcal for a p-value calibration that returns lower bounds on Bayes factors in favor of point null hypotheses.

Examples

# Interpretation of one Bayes factor (on the natural log scale)
bfactor_log_interpret(log(1.5))

# Interpretation of many Bayes factors (on the natural log scale)
bfactor_log_interpret(log(c(0.1, 1.2, 3.5, 13.9, 150)))

# Interpretation of many Bayes factors (on the log10 scale)
bfactor_log_interpret(log10(c(0.1, 1.2, 3.5, 13.9, 150)), base = 10)