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Glas and van der Linden (2003) show that the second part of this conclusion is not necessary, provided we model the situation appropriately Their model is based on two-stage (or strati ed) selection of a test from a pool of cloned items The steps are (1) selection of the families of items in the pool from which an item is to be administered, and (2) random sampling of an items from each selected family A graphical representation of the selection process is given by the Venn diagram in Figure 26 The selection of the families is assumed to be based on a statistical criterion; how this can be done is discussed below However, it is important that the selection of the items from the families is random; the model in the next section is based on this assumption In the hypothetical case depicted in Figure 26, we have much more variability between than within the families Intuitively, the proportion of the total variability that is between the families is an upper bound to the gain in the precision of ability estimation that can be made by optimizing the rst step in the item selection procedure using a statistical criterion The proportion that is within the families determines the loss in precision due to random item sampling in the second step

3GPP TR 23039 [78] is a technical report, not a technical speci cation The terms CS-based SMS and PS-based SMS, as sometimes used, are confusing, as SMS is by de nition packet switched

The proposed item-selection procedure suggests a two-level IRT model At the rst level, each of the individual items in each family is represented by a regular response model, such as the 3PL model in (21) At the second level, the distribution of the item parameters in each family is modeled These distributions are allowed to vary across families Speci cally, suppose we have a pool with families p 1; ; P and individual items ip 1; ; IP for family p The rst-level model is the 3PL model in (21), which describes the probability of success on item ip as a function of ability level and the item parameters For brevity, we denote the parameters as a vector nip aip ; bip ; cip The distribution of the responses of examinee j to

company without informing themselves of the CEO s motive to support the sale or role in establishing the purchase price, determining the intrinsic value of the company, and unnecessarily rushing the approval of sale without reviewing the proposed terms of the merger agreement Even though the company was sold at a substantial premium, the speedy approval process (a matter of hours not days) illustrated that the board did not take the time necessary to diligently consider the offer or any conflicts that might entice the CEO to support the sale Duty of loyalty generally speaks to a director s potential conflict of interest A director is required to act in good faith and in a manner reasonably and honestly believed to be in the best interests of the corporation and its shareholders to the exclusion of personal gain Where a conflict of interest exists, a director should recuse themselves from deliberation and decision making A case that exemplifies this duty can be found in the recent battle between Conrad Black and his board at Hollinger A special investigative report commissioned by the board of directors accused Black of misappropriating company assets After the headline grabbing accusations, Lord Black entered into an agreement with Hollinger to repay several million dollars in unauthorized payments He also agreed that he would sell control of the company only if such a transaction was equally beneficial to other stockholders among other things Despite this agreement, Lord Black privately entered negotiations to sell control of the company The courts held that Black breached his duty of loyalty to the company by failing to tell the board about this suitor s interest in buying the company, misleading the board about his dealings with the suitor, using confidential information to aid the transaction, and in attempting to subvert the loyalty of a financial advisor to a special committee of the board He also tried to amend the company bylaws covering asset sales It seems that the court found it difficult to accept the argument that these actions were made in the best interests of Hollinger s shareholders2 Incorporating the duty of care and duty of loyalty, Delaware s business judgment rule provides protection if a director acted on an informed basis, in good faith and in the honest belief that the action taken was in the best interest of the company 3 Most boards are covered under Delaware law, which allows corporations to include a provision in their charter restricting or eliminating a director s personal.

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item ip from family is thus determined by the probabilities Pr Uip j 1 p j ; nip 2:23