Create a covariance matrix for a panel design

Covariance structure accounts for the panel design and the four variance components: unit variation, period variation, unit by period interaction variation and index (or residual) variation. The model incorporates unit, period, unit by period, and index variance components. It also includes a provision for unit correlation and period autocorrelation.

cov_panel_dsgn(
  paneldsgn = matrix(50, 1, 10),
  nrepeats = 1,
  unit_var = NULL,
  period_var = NULL,
  unitperiod_var = NULL,
  index_var = NULL,
  unit_rho = 1,
  period_rho = 0
)

Arguments

paneldsgn

A matrix (dimensions: number of panels (rows) by number of periods (columns)) containing the number of units visited for each combination of panel and period. Default is matrix(50, 1, 10) which is a single panel of 50 units visited 10 times, typical time is a period.

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.

unit_var

The variance component estimate for unit. The default is NULL.

period_var

The variance component estimate for period The default is NULL.

unitperiod_var

The variance component estimate for unit by period interaction. The default is NULL.

index_var

The variance component estimate for index error. The default is NULL.

unit_rho

Unit correlation across periods. The default is 1.

period_rho

Period autocorrelation. The default is 0.

Value

A list containing the covariance matrix (cov) for the panel design, the input panel design (paneldsgn), the input nrepeats design (nrepeats.dsgn) and the function call.

Details

Covariance structure accounts for the panel design and the four variance components: unit variation, period variation, unit by period interaction variation and index (or residual) variation. Uses the model structure defined by Urquhart 2012.

If nrepeats is NULL, then no units sampled more than once in a specific panel, period combination) and then unit by period and index variances are added together or user may have only estimated unit, period and unit by period variance components so that index component is zero. It calculates the covariance matrix for the simple linear regression. The standard error for a linear trend coefficient is the square root of the variance.

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

power_dsgn

for power calculations of multiple panel designs

Author

Tony Olsen Olsen.Tony@epa.gov