### Table 4: Comparison of hierarchical models (linear and nonlinear) with non-hierarchical models (linear and nonlinear) based on protein fold classiflcation data.

2007

"... In PAGE 12: ... We refer to this models as dpCorMNL. Table4 presents the results for the two linear models (with and without hierarchy-base priors), and two nonlinear models (with and without hierarchy-based priors). In this table, \parent accu- racy quot; refers to the accuracy of models based on the four major structural classes, namely fi, fl, fi=fl.... ..."

### Table 2 Nonlinear models.

1998

"... In PAGE 16: ... Much of the emphasis will be on the choice of bandwidth and the new aspects brought in by using local polynomial approximation. A power experiment on a wide class of nonlinear models listed in Table2 has been conducted in Section 6.3.... In PAGE 18: ...Table2 , however, where M1(x) is approximately quadratic (see Figure 1), as can be expected the best result is achieved with T = 2 and h = 1. For the ^ L(V1)-tests the size tends to be too low.... In PAGE 18: ... If no corrections are made for this e ect, it will lead to conservative tests. Figure 5 shows the power of the ^ L(V )-tests for model la) of Table2 , and we see the same general trend as for the ^ L(M)-tests; the optimal h increases with T and the derivative. Here ^ L1(V1) also has some power for h = 1 because the variance is constant, not only linear, under the null hypothesis.... In PAGE 18: ... Here ^ L1(V1) also has some power for h = 1 because the variance is constant, not only linear, under the null hypothesis. ^ L0(V1) is much more robust than ^ L0(M1), and this is the case for the other models listed in Table2 as well. 6.... In PAGE 18: ... In particular when we have a nonlinear model, we do of course not want h = 1 to be chosen when T = 0 or T = 1, but with a small autocorrelation, this may well happen for T = 0. In fact h = 1 was chosen in 136 of 500 realizations of model lc) of Table2 which is clearly nonlinear (cf. Figure 1).... In PAGE 19: ... 6.3 A power experiment for a wide set of models We have performed a power experiment for the models listed in Table2 , where t N(0; 0:62) in model ld) - lf), t N(0; 0:72) in lg) - lj) and t N(0; 1) in the other models. Models la) - lj), aa) - ag) and Aa) - Ag) are discussed in Luukkonen et al.... In PAGE 36: ...Figure 1-2: Plots of ^ M1(x) (Figure 1) and ^ V1(e) (Figure 2) for the models listed in Table2 with n = 100 000. The kernel estimator with bandwidth h = 0:2 is used and each plot consists of two realizations.... In PAGE 36: ... The possible values for h is given at the vertical axes. Figure 7: The gure is based on 500 realizations of the models in Table2 . It shows the power of ^ LT (M1) with h cross-validated and n = 100, 250 and 204 for models la) - li), aa) - ag) and Aa) - Ag), respectively.... In PAGE 36: ...ower achieved in Hjellvik and Tj stheim (1995). The nominal size is 0.05. Figure 8: The gure is based on 500 realizations of the models in Table2 and shows the power of ^ LT (V1) with h cross-validated and n = 100, 250 and 204 for models la), aa) - ag) and Aa) - Ag), respectively.... In PAGE 37: ....05 for the standard normal distribution has been used. The model is Xt = t, the bandwidth is h = n?1=9 and the number of realizations are 500. Table2 : Various nonlinear models. Models la) - lj), aa) - ag) and Aa) - Ag) are discussed in Luukkonen et al.... ..."

Cited by 8

### Table 3: Number of accepted and rejected candidates in the presence of negative curvature 5 Conclusion We have exploited powerful and up-to-date technics in non-linear programming and adapted them to the problem of simultaneous estimation of hierarchical logit models. An optimiza- tion algorithm that is based on a quasi-Newton technic combined with trust region strat- egy, ensuring robustness and global convergence, and a modi ed preconditioned conjugate gradients iterations, exploiting non-concavity. The method has been applied to two numerical examples derived from real exercices, illustrating its major features, and clarifying the e ect of some algorithmic options. The algorithm described in this paper has been included in the HieLoW package (Bierlaire, 1994 and Bierlaire and Vandevyvere, 1995).

"... In PAGE 17: ... This rejection, followed by a reduction of the trust region size, insures the robustness of the algorithm when the model doesn apos;t t correctly the objective function or when singularity in the quadratic model is detected. If the number of rejections seems larger, especially when approximated Hessian is used (see column NO of Table3 , the number of instances where non-convexity is exploited is... In PAGE 18: ...01 0.1 1 10 Magnitude 0 5 10 15 20 25 30 35 Iteration Step Trust region Figure 5: Step magnitude and trust region size not negligible (column OK of Table3 ). Note that column -CURV of Table 3 gathers the same information as the last line in Table 1 and 2.... ..."

### Table 1. The Calculated Results for Analyzed Data-Set

2000

"... In PAGE 9: ... In order to have easy interpretable models, we have fixed the maximal number of terms in the equation to be equal to 8 and the maximum degree of polynoms to be equal to 3. The calculations performed using the select params option of the ANALYSIS are summarized in Table1 . The number of stored models was 3.... In PAGE 9: ... It was shown that the use of significant variables, as detected by MUSEUM, = improved PLS results (compare data in column 7 vs. column 6 in Table1 ). The similar tendency was also observed if only variables found to be relevant by the PNN algorithm were used in the cross-validation calculations (compare the last and 7 columns of Table 1).... In PAGE 12: ... b Number of significant PLS components. c The cross-validated q2 calculated using input variables optimized by MUSEUM approach (unless not stated otherwise the PLS results are from Table1 and 15 of (2)). d Number of input variables selected by PNN.... ..."

Cited by 2

### Table 2. Distribution of number of individuals within households No. of individuals

"... In PAGE 4: ... Although it does not make sense to attempt to esti- mate components of variation attributable to indi- viduals and households using data from one-person households (as the two eC128ects cannot be disen- tangled), one-person households were retained in the analysis as they contribute to the estimates of the covariates of alcohol consumption and to area variations in consumption. The distribution of num- bers of individuals within households is given in Table2 . The vast majority of the sample live in two-person households.... ..."

### Table 1 Linear preprocessing for nonlinear models

2005

"... In PAGE 9: ... We thus obtain eight different methods that correspond to all possible combinations of three concepts above: the first one is the linear preprocessing (PCA or PLS), the second one is the optional whitening and the last part is the nonlinear model (RBFN or LS-SVM). Methods are sum- marized in Table1 (see also Fig. 4).... ..."

### Table 3: Nonlinear dynamic model with trend

"... In PAGE 17: ... Turning to the model of income dynamics, Table 2 gives our estimates of equation (4) without the trend (suppressing the constant term in 4).7 Table3 gives the results including the 7 The sample mean annual income is Yuan 446 per capita at 1985 prices (with a standard deviation of 264), while the corresponding mean for expenditure is Yuan 345 (standard deviation of 166).... ..."

### Table 3: Nonlinear dynamic model with trend

"... In PAGE 14: ... Turning to the model of income dynamics, Table 2 gives our estimates of equation (4) without the trend (suppressing the constant term in 4).7 Table3 gives the results including the 7 The sample mean annual income is Yuan 446 per capita at 1985 prices (with a standard deviation ... ..."

### Table 4. Core Processes of the Nonlinear Model

2005

"... In PAGE 14: ...Opening, Orientation, and Consolidation, culminating in a summary of the whole model. The final list of contextual interactions appears in Table 3, and a list of the core processes appears in Table4 . [Insert Figure 1, Table 3, and Table 4 here] External Context Information behaviour is not isolated from the context within which the information seeker works.... In PAGE 14: ... The final list of contextual interactions appears in Table 3, and a list of the core processes appears in Table 4. [Insert Figure 1, Table 3, and Table4 here] External Context Information behaviour is not isolated from the context within which the information seeker works. Major external influences were categorised as Social and Organisational, Time, The Project, Navigation Issues and Access to Sources.... ..."

Cited by 3