Internal function that generates plots of data and model results.
Description
seawaveQPlots is usually called from within
fitMod
but can be invoked directly. It
generates plots of data and model results, as well as
diagnostic plots, and returns the observed and predicted
concentrations so that users may plot the concentrations
using their own functions.
Usage
1 2 3  seawaveQPlots(stpars, cmaxt, tseas, tseaspr, tndlin,
tndlinpr, cdatsub, cavdat, cavmat, clog, centmp,
yrstart, yrend, tyr, tyrpr, pnames, tanm, mclass = 1)

Arguments
stpars 
is a matrix of information about the best
seawaveQ model for the concentration data, see

cmaxt 
is the decimal season of maximum chemical concentration. 
tseas 
is the decimal season of each concentration value in cdatsub. 
tseaspr 
is the decimal season date used to model concentration using the continuous data set cavdat. 
tndlin 
is the decimal time centered on the midpoint of the trend for the sample data, cdatasub. 
tndlinpr 
is is the decimal time centered on the midpoint of the trend for the continuous data, cavdat. 
cdatsub 
is the concentration data 
cavdat 
is the continuous (daily) ancillary data 
cavmat 
is a matrix containing the continuous ancillary variables. 
clog 
is a vector of the base10 logarithms of the concentration data. 
centmp 
is a logical vector indicating which concentration values are censored. 
yrstart 
is the starting year of the analysis (treated as January 1 of that year). 
yrend 
is the ending year of the analysis (treated as December 31 of that year). 
tyr 
is a vector of decimal dates for the concentration data 
tyrpr 
is a vector of decimal dates for the continuous ancillary varaibles. 
pnames 
is the parameter (waterquality constituents) to analyze (if using USGS parameters, omit the the starting 'P', such as "00945" for sulfate). 
tanm 
is an a character identifier that names the trend analysis run. It is used to label output files. 
mclass 
has not been implemented yet, but will provide additional model options. 
Value
a pdf file containing plots of the data and modeled concentrations and regression diagnostic plots and a list containing the observed concentrations (censored and uncensored) and the predicted concentrations used for the plot.
Note
The plotting position used for representing censored
values in the plots produced by
seawaveQPlots
is an important consideration
for interpreting model fit. Plotting values obtained by
using the censoring limit, or something smaller such as
onehalf of the censoring limit, produce plots that are
difficult to interpret if there are a large number of
censored values. Therefore, to make the plots more
representative of diagnostic plots used for standard
(noncensored) regression, a method for substituting
randomized residuals in place of censored residuals was
used. If a logtransformed concentration is censored at
a particular limit, logC < L
, then the residual
for that concentration is censored as well, logC 
fitted(logC) < L  fitted(logC) = rescen
. In that case,
a randomized residual was generated from a conditional
normal distribution
resran < scl *
qnorm(runif(1) * pnorm(rescen / scl))
,
where scl
is the scale parameter from the survival regression
model, pnorm
is the R function for computing
cumulative normal probabilities, runif
is the R
function for generating a random variable from the
uniform distribution, and qnorm
is the R function
for computing quantiles of the normal distribution. Under
the assumption that the model residuals are uncorrelated,
normally distributed random variables with mean zero and
standard deviation scl, the randomized residuals
generated in this manner are an unbiased sample of the
true (but unknown) residuals for the censored data. This
is an application of the probability integral transform
(Mood and others, 1974) to generate random variables from
continuous distributions. The plotting position used a
censored concentration is fitted(logC) + resran
.
Note that each time a new model fit is performed, a new
set of randomized residuals is generated and thus the
plotting positions for censored values can change.
Author(s)
Aldo V. Vecchia and Karen R. Ryberg
References
Mood, A.M., Graybill, F.A., and Boes, D.C., 1974, Introduction to the theory of statistics (3d ed.): New York, McGrawHill, Inc., 564 p.
Examples
1 2 3 4 5 6 7  data(swData)
myPlots < seawaveQPlots(stpars=examplestpars, cmaxt=0.4808743,
tseas=exampletseas, tseaspr=exampletseaspr, tndlin=exampletndlin,
tndlinpr=exampletndlinpr, cdatsub=examplecdatsub, cavdat=examplecavdat,
cavmat=examplecavmat, clog=exampleclog, centmp=examplecentmp,
yrstart=1995, yrend=2003, tyr=exampletyr, tyrpr=exampletyrpr,
pnames=c("04041"), tanm="examplePlots04041")

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