### Table I. Derivatives of permanent environmental standard deviations with respect to parameters of functions modelling changes in variances or standard deviations with time.

### Table 2. Log likelihood values (logL; +45,000 for complete data and +10,000 for subset) and corresponding information criteria (AIC : Akaike Information Criterion, BIC : Schwarz Bayesian Information Criterion, HQC : Hannan and Quinn Criterion, and CAIC : Consistent AIC; -90,000 and -20,000, respectively) for analyses with different orders of polynomial fit (k) and variance function to model measurement error variances (figures in bold denoting best model identified by each criterion).

"... In PAGE 7: ....2.1. Order of fit Table2 summarises maximum log likelihood values and corresponding information criteria for phenotypic analyses. Likelihoods increased significantly with k (at 5% signicance level), even for k = 10 with 114 pa- rameters, i.... In PAGE 9: ....3.1. Subset of data Genetic analyses considering only a subset of the data were carried out fitting Legendre polynomials to order k = 4;6 and 8 for a RRM ignoring maternal genetic effects (Model G1), and k = 4 for a model including the latter (Model G2). Corresponding values for log L and information criteria are given in Table2 . Again, LRTs favoured the model with the highest number of parameters, while information criteria were minimum for orders of fit of k = 4 or 6.... In PAGE 10: ... In doing so, choices of k were guided by results from analyses carried out so far, and not all models were fitted for both data sets. Values for logL and corresponding information criteria for the different analyses are given in Table2 . As above, fitting maternal genetic effects for WOK did not increase logL significantly (k = 4464 vs.... ..."

### Table 1. A quantitative comparison of each model showing the variance explained by each mode. F is the value of the objective function and VT is the total variance.

2002

Cited by 34

### Table 1. A quantitative comparison of each model showing the variance explained by each mode. BY D1CXD2 is the value of the objective function and CE CC is the total variance.

### Table 4: Simulation Speed and Variance

1999

"... In PAGE 15: ... IV. Substitution Patterns Table4 provides an illustration of the substitution patterns that are implied by each of the models. In particular, the table gives the probabilities from each of the four models under various scenarios compared with a base situation.... In PAGE 16: ...Table4 are not forecasts, the differences in the substitution patterns that arise under the different models will also occur in forecasting since these differences are intrinsic to the model specifications. We first describe the differences between the standard logit and the mixed logit in column 2 of Table 2, called mixed logit A.... In PAGE 16: ... We then describe differences with the pure probit and the mixed logit in column 4, called mixed logit B. In part 1 of Table4 , a mini electric car is introduced to a base situation consisting of five gas cars. The logit model, because of the iia property, implies that the new electric car will draw proportionately from all five of the gas cars.... In PAGE 17: ...relative to existing products, is potentially important in forecasting penetration rates for any new product, but especially for products that are expected to satisfy niche markets. For part 2 of Table4 , a second electric car in introduced, comparable in size to a gas subcompact. The previous scenario (five gas cars and a mini electric car) is taken as the base.... In PAGE 19: ... The log of the simulated probability is not unbiased for the log of the true probability; rather, given the log transformation, it is biased downward for a finite number of replications, with the bias decreasing as the number of replications increases. The figures in Table4 are consistent with these facts. Whether the bias can be considered large depends on the perspective that one takes.... In PAGE 20: ... We performed similar calculations for the pure probit. The results are given in the last column of Table4 . The variance in the average probability and the log-likelihood function is somewhat smaller for the GHK simulator with 50 replications than the mixed logit with the same number of replications.... In PAGE 21: ... Nevertheless, the recursive nature of the GHK simulator (where the range for the random draw for one alternative depends on the value of previous draws for other alternatives) is inherently slow compared to simulators, like the mixed logit simulator, which draw simultaneously from unrestricted ranges. In light of these issues, the results in Table4 are perhaps best interprested as simply an indication that the mixed logit simulator is reasonably accurate compared to the GHK simulator, particularly for given computer time.... ..."

Cited by 25

### Table 12: Values of the cross-validation criterion C for all combinations of a regression and a variance model in Example 5. Regression Variance model

"... In PAGE 26: ...55) and the quadratic variance model (2.9) (see Table12 ). That is, if an estimation of the regression function would be of interest, a WLSE calculated for the model (1.... ..."

### Table 12: Values of the cross-validation criterion C for all combinations of a regression and a variance model in Example 5. Regression Variance model

"... In PAGE 26: ...55) and the quadratic variance model (2.9) (see Table12 ). That is, if an estimation of the regression function would be of interest, a WLSE calculated for the model (1.... ..."

### Table 12: Values of the cross-validation criterion C for all combinations of a regression and a variance model in Example 5. Regression Variance model

"... In PAGE 26: ...55) and the linear variance model (2.12) (see Table12 ). That is, if an estimation of the regression function would be of interest, a WLSE calculated for the model (1.... ..."

### Table 2: Values of the cross-validation criteria C and CC for all combinations of a regression and a variance model. Regression Variance model

1995

"... In PAGE 16: ...The results reported in Table2 for both the cross validation criterion C for prediction and the calibration criterion CC clearly indicate that variance modelling and use of WLSE leads to an improvement if the objective is prediction or estimation of the regression function while for calibration an OLSE may be preferred. Note that the best model for prediction, (2.... ..."

Cited by 3

### Table 2. Variance ratios for the M=M=s=0 model with = 1 as a function of and s. The simulation run length is 106=s with 20 batches in each case (corresponding to an expected number of arrivals equal to ( =s)106).

1999

"... In PAGE 18: ... A key point is that everything is not captured by the linear controls: The di erences between the natural and indirect estimators are not removed by simply using linear controls. In Table2 we give variance ratios for the M=M=s=0 model with = 1 as a function of and s. The intent here is to show the impact of system size as well as loading.... ..."

Cited by 9