Reliability of reflectance measures in passive filters

Measurements of optical reflectance in passive filters impregnated with a reactive chemical solution may be transformed to ozone concentrations via a calibration curve and constitute a low cost alternative for environmental monitoring, mainly to estimate human exposure. Given the possibility of errors caused by exposure bias, it is common to consider sets of m filters exposed during a certain period to estimate the latent reflectance on n different sample occasions at a certain location. Mixed models with sample occasions as random effects are useful to analyze data obtained under such setups. The intra-class correlation coefficient of the mean of the m measurements is an indicator of the reliability of the latent reflectance estimates. Our objective is to determine m in order to obtain a pre-specified reliability of the estimates, taking possible outliers into account. To illustrate the procedure, we consider an experiment conducted at the Laboratory of Experimental Air Pollution, University of Sمo Paulo, Brazil (LPAE/FMUSP), where sets of m = 3 filters were exposed during 7 days on n = 9 different occasions at a certain location. The results show that the reliability of the latent reflectance estimates for each occasion obtained under homoskedasticity is km = 0.74. A residual analysis suggests that the within-occasion variance for two of the occasions should be different from the others. A refined model with two within-occasion variance components was considered, yielding km = 0.56 for these occasions and km = 0.87 for the remaining ones. To guarantee that all estimates have a reliability of at least 80% we require measurements on m = 10 filters on each occasion.