Log-odds ratio

Calculates the log-odds ratio effect size index, with or without bias correction (Pustejovsky, 2015)

LOR(
  A_data,
  B_data,
  condition,
  outcome,
  baseline_phase = NULL,
  intervention_phase = NULL,
  improvement = "increase",
  scale = "percentage",
  intervals = NULL,
  D_const = NULL,
  bias_correct = TRUE,
  confidence = 0.95
)

Arguments

A_data

vector of numeric data for A phase. Missing values are dropped.

B_data

vector of numeric data for B phase. Missing values are dropped.

condition

vector identifying the treatment condition for each observation in the series.

outcome

vector of outcome data for the entire series.

baseline_phase

character string specifying which value of condition corresponds to the baseline phase. Defaults to first observed value of condition.

intervention_phase

character string specifying which value of condition corresponds to the intervention phase. Defaults to second unique value of condition.

improvement

character string indicating direction of improvement. Default is "increase".

scale

character string indicating the scale of the outcome variable. Must be either "percentage" for percentages with range 0-100 or "proportion" for proportions with range 0-1. If a vector, the most frequent unique value will be used. "percentage" is assumed by default.

intervals

for interval recording procedures, the total number of intervals per observation session. If a vector, the mean number of intervals will be used.

D_const

constant used for calculating the truncated sample mean (see Pustejovsky, 2015). If a vector, the mean value will be used.

bias_correct

logical value indicating whether to use bias-correction. Default is TRUE.

confidence

confidence level for the reported interval estimate. Set to NULL to omit confidence interval calculations.

Value

A data.frame containing the estimate, standard error, and approximate confidence interval.

Details

The odds ratio parameter is the ratio of the odds of the outcome. The log-odds ratio is the natural logarithm of the odds ratio. This effect size is appropriate for outcomes measured on a percentage or proportion scale. Unlike the LRRd and LRRi, the LOR is symmetric in valence, so that the LOR for an positively-valenced outcome is equal to -1 times the LOR calculated after reversing the scale of the outcome so that it is negatively valenced.

Without bias correction, the log-odds ratio is estimated by substituting the sample mean level in each phase in place of the corresponding parameter. A delta-method bias correction to the estimator is used by default.

The standard error of LOR is calculated based on a delta-method approximation, allowing for the possibility of different degrees of dispersion in each phase. The confidence interval for LOR is based on a large-sample (z) approximation.

To account for the possibility of sample means of zero, a truncated mean is calculated following the method described in Pustejovsky (2015). Truncated sample variances are also calculated to ensure that standard errors will be strictly larger than zero. The truncation constant depends on the total number of intervals per session (or the total number of items for other percentage/proportion scales). The arguments scale and intervals must be specified in order to calculate an appropriate truncation constant. For outcomes measured using continuous recording procedures, set intervals equal to 60 times the length of the observation session in minutes.

References

Pustejovsky, J. E. (2015). Measurement-comparable effect sizes for single-case studies of free-operant behavior. Psychological Methods, 20(3), 342--359. doi:doi:10.1037/met0000019

Examples

A_pct <- c(20, 20, 25, 25, 20, 25)
B_pct <- c(30, 25, 25, 25, 35, 30, 25)
LOR(A_data = A_pct, B_data = B_pct,
    scale = "percentage", intervals = 20, bias_correct = FALSE)
#>    ES       Est         SE   CI_lower  CI_upper
#> 1 LOR 0.2852038 0.09790282 0.09331776 0.4770898
LOR(A_data = A_pct, B_data = B_pct,
    scale = "percentage", intervals = 20)
#>    ES       Est         SE   CI_lower  CI_upper
#> 1 LOR 0.2852854 0.09790282 0.09339935 0.4771713

LOR(A_data = A_pct, B_data = B_pct, scale = "percentage")
#>    ES       Est         SE   CI_lower  CI_upper
#> 1 LOR 0.2852854 0.09790282 0.09339935 0.4771713
LOR(A_data = A_pct / 100, B_data = B_pct / 100, scale = "proportion")
#>    ES       Est         SE   CI_lower  CI_upper
#> 1 LOR 0.2852854 0.09790282 0.09339935 0.4771713
LOR(A_data = A_pct, B_data = B_pct, scale = "percentage", improvement = "decrease")
#>    ES        Est         SE   CI_lower    CI_upper
#> 1 LOR -0.2852854 0.09790282 -0.4771713 -0.09339935