Upper Mississippi River Restoration Program Long Term Resource Monitoring

Estimating means and temporal trends using LTRM data: details with examples

Estimating temporal trends for a single stratum

Estimating temporal trends from a single stratum represents the simplest case for estimating temporal trends from LTRMP data. In this case, strata effects may be ignored.

Estimating temporal trends for a single stratum using fish data

Here we illustrate estimating temporal trends in bluegill catch per unit effort in the backwater contiguous shoreline (BWC-S) stratum of Navigation Pool 8 from 1993-2004. SAS does not currently offer a survey procedure for counts, so we use SUDAAN. However, SUDAAN requires preprocessing of LTRMP data, which we do using SAS data statements. The following code creates a “centered” year variable by subtracting a value—any value—that occurs within the sampling period (not centering will yield an intercept that represents an extrapolation to year 0 AD). We then create an effort variable ("effmin15") that is in units of 15 minutes. The "sweight" variable is needed because SUDAAN’s LOGLINK procedure requires a weight statement (even if that variable is, as here, constant). The "where" statement is added to this code because SUDAAN doesn’t support "where" (or "by") statements.

data BLGLP8b;
set BLGLP8;
yearctr=year-2000;
effmin15=effmin/15;
sweight=1;
where period ge 2 and fstation=2 and stratum2="BWC-S";
run;
proc sort data=BLGLP8b; by year; run;

After running the code above to generate a modified dataset, we submit the dataset to SUDAAN for trend estimation. The code below estimates trends in the mean on the log scale (the data themselves are not log transformed).  Estimating parameters from count data on the log scale yields advantages, including that predicted count means cannot be negative. The procedure ("proc") statement notes that we treat years as sampled with replacement ("design = wr"). The nest statement notes that data are nested within years which occur within a single ("_one_") population (corresponding here to Navigation Pool 8).  The offset uses "effmin," the effort variable created above.

proc loglink data=BLGLP8b filetype=sas design=wr;
nest _one_ year;
model catch = yearctr / offset=effmin15;
weight sweight;
print beta="Beta" sebeta="SE" lowbeta="Low 95%" upbeta="Up 95%" t_beta="t:beta=0"
p_beta="p-value" / betafmt=f8.4 sebetafmt=f8.4 lowbetafmt=f8.4 upbetafmt=f8.4
t_betafmt=f8.4 p_betafmt=f7.4;
run;

Output from the SUDAAN code is presented below. Note that the trend estimate ("Beta") and confidence interval estimates ("Low 95%", "Up 95%") are on the log scale, and may be converted to the measurement scale by exponentiation. Doing so yields exp(0.0714) (exp(-0.0715), exp(0.2143)) or 1.07 (0.93, 1.24) per year. The point estimate represents a multiplicative effect, also called an "effect modifier." In this example, our best estimate of a constant multiplicative change over the period 1993 through 2004 is an increase of 7% per year. (Of course, based on the t statistic and the 95% confidence interval, we have little confidence in the direction of this trend estimate.)

Variance Estimation Method: Taylor Series (WR)
SE Method: Robust (Binder, 1983)
Working Correlations: Independent
Link Function: Log
Response variable CATCH: CATCH
Offset variable EFFMIN15: EFFMIN15
by: Independent Variables and Effects.

Estimating temporal trends for a single stratum using macroinvertebrate data

Single-stratum temporal trends in macroinvertebrate data may be estimated using the same code as was used for the bluegill example above. The offset value is 0.053 m² / ponar grab.

Estimating temporal trends for a single stratum using vegetation data

We illustrate the estimation of temporal trends for a single stratum using wild celery data from the impounded stratum of Pool 13 (1998 – 2008). As with the above analyses, we begin by creating a centered year variable.

data VAAM3FS3b;
set VAAM3FS3;
yearctr=year-2000;

Trends in percent frequency of detection may be estimated using the following SAS code:

proc surveylogistic data=VAAM3FS3b;
cluster year;
model sitedetect = yearctr / s;
where pool = “13” and strat= “IMP”;
run;

If we add a class statement (e.g., "class cov_nrf;") to the above surveylogistic code, we can estimate trends in multi-category data (e.g., in cover data).

Estimating temporal trends for a single stratum using water data

Trends in water data from a single stratum may be estimated using SAS’ survey regression procedure. Here we illustrate estimating temporal trends in chlorophyll a in the impounded stratum of Pool 13 (1993 – 2008). As is typical we center year by subtracting a value within the sampling period.

data WQall2;
set WQall;
yearctr=year-2000;

proc surveyreg data=WQall2;
cluster year;
model chlf = yearctr / s;
where strat=”IMP” and fs=3;
run;

The resulting trend estimate of -0.33 mean mg chlorophyll a per L per year cannot be distinguished from zero (see below).

Contact: Questions or comments may be directed to Brian Gray, LTRM statistician, Upper Midwest Environmental Sciences Center, La Crosse, Wisconsin, at brgray@usgs.gov.