Tables

TABLE 1: FITTING THE LINEAR MODEL
		CARP
		LAKE ALLEGAN					PLAINWELL IMPOUNDMENT
Source		DF	Type III SS	MSE	F Value	Pr > F	DF	Type III SS	MSE	F Value	Pr > F
Full Model	log(lipid)	1	0.203	0.203	0.76	0.3862	1	0.207	0.207	0.96	0.3310
	log(length)	1	0.745	0.745	2.77	0.0983	1	1.245	1.245	5.76	0.0188
	yr	8	7.854	0.982	3.65	0.0007	6	1.116	0.186	0.86	0.5281
	log(length)*yr	8	7.061	0.883	3.28	0.0018	6	1.056	0.176	0.81	0.5620
	log(length)*log(lipid)	1	0.236	0.236	0.88	0.3511	1	0.130	0.130	0.60	0.4397
	log(lipid)*yr	8	2.629	0.329	1.22	0.2905	6	1.119	0.186	0.86	0.5263
	log(lipid)log(length)yr	8	2.692	0.337	1.25	0.274	6	1.072	0.179	0.83	0.5532
No Three-way Interaction	log(lipid)	1	4.788	4.788	17.56	<.0001	1	0.055	0.055	0.26	0.6135
	log(length)	1	1.773	1.773	6.50	0.0117	1	0.854	0.854	4.00	0.0487
	yr	9	7.879	0.875	3.21	0.0014	6	2.932	0.489	2.29	0.0429
	log(length)*yr	9	7.251	0.806	2.96	0.0029	6	2.879	0.480	2.25	0.0465
	log(lipid)*log(length)	1	4.221	4.221	15.49	0.0001	1	0.020	0.020	0.09	0.7593
	log(lipid)*yr	9	5.203	0.578	2.12	0.0308	6	2.239	0.373	1.75	0.1200
		SMALLMOUTH BASS
		LAKE ALLEGAN					PLAINWELL IMPOUNDMENT
Source		DF	Type III SS	MSE	F Value	Pr > F	DF	Type III SS	MSE	F Value	Pr > F
Full Model	log(lipid)	1	0.020	0.020	0.1	0.7576	1	0.001	0.001	0.01	0.9425
	log(length)	1	0.012	0.012	0.06	0.8081	1	0.011	0.011	0.05	0.8311
	yr	3	0.257	0.086	0.41	0.7453	2	0.036	0.018	0.07	0.9288
	log(length)*yr	3	0.302	0.101	0.49	0.6946	2	0.029	0.014	0.06	0.9423
	log(length)*log(lipid)	1	0.031	0.031	0.15	0.7004	1	0.000	0.000	0.00	0.9955
	log(lipid)*yr	3	0.120	0.040	0.19	0.9008	2	0.172	0.086	0.36	0.7013
	log(lipid)log(length)yr	3	0.124	0.041	0.2	0.8969	2	0.171	0.086	0.36	0.7031
No Three-way Interaction	log(lipid)	1	0.418	0.418	2.14	0.1515	1	0.062	0.062	0.27	0.6064
	log(length)	1	0.019	0.019	0.10	0.7555	1	0.640	0.640	2.77	0.1052
	yr	4	0.552	0.138	0.71	0.5920	2	1.052	0.526	2.28	0.1179
	log(length)*yr	4	0.590	0.147	0.75	0.5607	2	1.110	0.555	2.40	0.1056
	log(lipid)*log(length)	1	0.473	0.473	2.42	0.1273	1	0.091	0.091	0.39	0.5355
	log(lipid)*yr	4	0.755	0.189	0.97	0.4366	2	0.158	0.079	0.34	0.7124
No Interactions	log(lipid)	1	1.159	1.159	5.58	0.0221	1	4.187	4.187	17.06	0.0002
	log(length)	1	0.031	0.031	0.15	0.7029	1	0.058	0.058	0.24	0.6283
	yr	4	21.076	5.269	25.37	<.0001	3	2.023	0.674	2.75	0.0557

TABLE 2: FITTED TIME TREND AND PREDICTED MEAN FOR 2010
		SMALLMOUTH BASS		CARP
		LAKE ALLEGAN	PLAINWELL IMPOUNDMENT	LAKE ALLEGAN	PLAINWELL IMPOUNDMENT
Adjustment Values	Length (cm)	34.8115	34.8115	50.5159	50.5159
Adjustment Values	Lipid (g/kg)	0.9753	0.9753	3.4218	3.4218
Model Parameter Estimates	C₁₉₉₀	2.3739	2.1187	6.1205	4.3600
	θ	0.8096	0.9222	1.3120	1.1799
	k	0.1548	0.0827	0.0960	0.0538
	σ	0.5200	0.4626	0.7304	0.4288
Predictions	lcl	0.0353	0.1312	0.2397	0.5362
	μ₂₀₁₀	0.0623	0.4017	0.6088	1.2493
	ucl	0.2077	0.9353	0.9658	1.9887
Adjustment values refer to the length and lipid values used to adjust the residuals from the initial linear models and put all fish from each species on the same scale. The model parameter estimates are the maximum likelihood estimates for the parameters of the mixed order model and the lognormal shape parameter s. Lcl and ucl are the lower and upper 95% profile likelihood based confidence limits for the maximum likelihood estimate of m₂₀₁₀, the mean PCB concentrations in 2010.

TABLE 3: SIMULATION RESULTS
Simulation Type	Base Dataset	Failed	Covered	Missed	%Coverage
Lognormal Error	Lake Allegan	4	958	38	96.2
Lognormal Error	Plainwell Impoundment	5	988	7	99.3
Empirical Distribution	Lake Allegan	4	994	2	99.8
Empirical Distribution	Plainwell Impoundment	7	990	3	99.7
Full Procedure Empirical Distribution	Lake Allegan	13	729	258	73.9
Full Procedure Empirical Distribution	Plainwell Impoundment	3	776	221	77.8
1000 datasets were generated for each simulation. For each generated datatset, it was noted whether the procedures failed to converge (Failed), the generated confidence interval contained the true value (Covered), or did not contain the true mean (Missed). A Monte Carlo estimate for the coverage of confidence interval (%Coverage) is given by Covered/[Missed+Covered].