power_dsgn function

Power calculation for multiple panel designs

Calculates the power for trend detection for one or more variables, for one or more panel designs, for one or more linear trends, and for one or more significance levels. The panel designs create a covariance model where the model includes variance components for units, periods, the interaction of units and periods, and the residual (or index) variance.

power_dsgn(
  ind_names,
  ind_values,
  unit_var,
  period_var,
  unitperiod_var,
  index_var,
  unit_rho = 1,
  period_rho = 0,
  paneldsgn,
  nrepeats = NULL,
  trend_type = "mean",
  ind_pct = NULL,
  ind_tail = NULL,
  trend = 2,
  alpha = 0.05
)

Arguments

• ind_names: Vector of indicator names

• ind_values: Vector of indicator mean values

• unit_var: Vector of variance component estimates for unit variability for the indicators

• period_var: Vector of variance component estimates for period variability for the indicators

• unitperiod_var: Vector of variance component estimates for unit by period interaction variability for the indicators

• index_var: Vector of variance component estimates for index (residual) error for the indicators

• unit_rho: Correlation across units. Default is 1.

• period_rho: Correlation across periods. Default is 0.

• paneldsgn: A list of panel designs each as a matrix. Each element of the list is a matrix with dimnames (dimensions: number of panels (rows) by number of periods (columns)) containing the number of units visited for each combination of panel and period. Dimnames for columns must be able to be coerced into an integer (e.g., 2016). All designs must span the same number of periods. Typically, the panel designs are the output of the function revisit_dsgn.

• nrepeats: Either NULL or a list of matrices the same length as paneldsgn specifying the number of revisits made to units in a panel in the same period for each design. Specifying NULL indicates that number of revisits to units is the same for all panels and for all periods and for all panel designs. The default is NULL, a single visit. Names must match list names in paneldsgn.

• trend_type: Trend type is either "mean" where trend is applied as percent trend in the indicator mean or "percent" where the trend is applied as percent trend in the proportion (percent) of the distribution that is below or above a fixed value. Default is trend_type="mean"

• ind_pct: When trend_type is equal to "percent", a vector of the values of the indicator fixed value that defines the percent. Default is NULL

• ind_tail: When trend_type is equal to "percent", a character vector with values of either "lower" or "upper" for each indicator. "lower"

  states that the percent is associated with the lower tail of the distribution and "upper" states that the percent is associated with the upper tail of the distribution. Default is NULL.

• trend: Single value or vector of assumed percent change from initial value in the indicator for each period. Assumes the trend is expressed as percent per period. Note that the trend may be either positive or negative. The default is 2.

• alpha: Single value or vector of significance level for linear trend test, alpha, Type I error, level. The default is 0.05.

Returns

A list with components trend_type, ind_pct, ind_tail, trend values across periods, periods (all periods included in one or more panel designs), significance levels, a five-dimensional array of power calculations (dimensions: panel, design names, periods, indicator names, trend names, alpha_names), an array of indicator mean values for each trend and the function call.

Details

Calculates the power for detecting a change in the mean for different panel design structures. The model incorporates unit, period, unit by period, and index variance components as well as correlation across units and across periods. See references for methods.

Examples

# Power for rotating panel with sample size 60
power_dsgn("Variable_Name",
  ind_values = 43, unit_var = 280, period_var = 4,
  unitperiod_var = 40, index_var = 90, unit_rho = 1, period_rho = 0,
  paneldsgn = list(NoR60 = revisit_dsgn(20,
    panels = list(NoR60 = list(
      n = 60, pnl_dsgn = c(1, NA),
      pnl_n = NA, start_option = "None"
    )), begin = 1
  )),
  nrepeats = NULL, trend_type = "mean", trend = 1.0, alpha = 0.05
)

References

Urquhart, N. S., W. S. Overton, et al. (1993) Comparing sampling designs for monitoring ecological status and trends: impact of temporal patterns. In: Statistics for the Environment. V. Barnett and K. F. Turkman. John Wiley & Sons, New York, pp. 71-86.

Urquhart, N. S. and T. M. Kincaid (1999). Designs for detecting trends from repeated surveys of ecological resources. Journal of Agricultural, Biological, and Environmental Statistics, 4(4) , 404-414.

Urquhart, N. S. (2012). The role of monitoring design in detecting trend in long-term ecological monitoring studies. In: Design and Analysis of Long-term Ecological Monitoring Studies. R. A. Gitzen, J. J. Millspaugh, A. B. Cooper, and D. S. Licht (eds.). Cambridge University Press, New York, pp. 151-173.

See Also

• ppd_plot: to plot power curves for panel designs

Author(s)

Tony Olsen Olsen.Tony@epa.gov