Random Effects Logistic Regression Model for Ranking Efficiency in Data Envelopment Analysis

Transcription

1 Random Effets Logisti Regression Model for Ranking Effiieny in Data Envelopment Analysis So Young Sohn Department of Information & Industrial Systems Engineering Yonsei University, 34 Shinhon-dong, Seoul , Republi of Korea Abstrat Ranking effiieny based on DEA results an be used for grouping DMUs. The resulting group membership an be partly related to environmental harateristis of DMU, whih are not used either as input or output. Utilizing the expert knowledge on super effiieny DEA results, we propose a multinomial Dirihlet regression model whih an be used for the purpose of seletion of new projets. A ase study is presented in the ontext of ranking analysis of new information tehnology ommerialization projets. It is expeted that our proposed approah an omplement the DEA ranking results with environmental fators and at the same time it failitates the predition of effiieny of new DMUs with only given environmental harateristis. Keywords DEA, Ranking analysis, Multinomial Dirihlet regression model, IT projet seletion Introdution Data Envelopment Analysis (DEA, initially studied by harnes et al. (978, is a methodology used to measure and evaluate the relative effiieny of a set of homogeneous deision-making-units (DMUs with multiple inputs and outputs. However, several limitations of DEA have been indiated: the risk of evaluating a DMU only with inputs and outputs and inability of effiieny predition without inputs and aomplished outputs at the planning stage. In an effort to resolve these limitations, Sohn and hoi (2005 suggested a random effets logisti regression model based on the DEA results. The authors inorporated two different outomes of the DEA results (effiient DMU or orresponding author. Tel.: ; fax: ; sohns@yonsei.a.kr (S. Y. Sohn. 8

2 Ranking Effiieny in Data Envelopment Analysis 9 ineffiient DMU with a random effets logisti model that an aommodate not only the environmental harateristis whih were left out from the DEA but also the unertainty that annot be explained by suh environmental fators. The proposed random effets model an be used for the predition of effiieny of a new DMU only with given environmental harateristi s. What their model did not onsider was the multi ategory of DEA outomes. Several ranking approahes based on DEA have been proposed (Sexton (986, Andersen & Petersen (993 and Friedman & Sinuany-Stern (997. One of the widely used ranking methods is the super-effiieny tehniue, suggested by Andersen and Petersen (993, whih ranks DMUs through the exlusion of the unit being sored from the original DEA model. Upon availability of the ranking information, DMUs an be ategorized into several groups. For instane, finished R&D projets an be rated as aepted, undetermined, or failed groups. In this paper, we inorporate the group membership results with a random effets model that an aommodate not only the environmental harateristis whih were left out from the super effiieny ranking analysis but also the unertainty that annot be explained by suh environmental fators. Random effets model has been freuently used to aommodate both between luster variation as well as within luster variation (Sohn, 993, 996, 997, 999, In our ase, the between luster variation orresponds to the variation due to environmental fators while the within luster variation reflets the random variation due to unertainty that annot be explained by suh environmental fators. Our proposed approah is illustrated in the ontext of ranking analysis on various tehnology ommerialization projets lustered with respet to the type of information tehnology (IT, related R&D developer and its reeiver (Sohn and Moon, It is expeted that our approah an omplement the effiieny-based ranking results with environmental fators and at the same time it failitates the seletion of new tehnology development senarios at the planning stage. The organization of this paper is as follows. In setion 2, random effets model for DEA with multi ategorial results is proposed. Setion 3 presents the ase study. Setion 4 ontains onlusions and future researh issues. 2 Random effets model for DEA with multi ategory outome The general DEA model suh as R (harnes et al., 978 and B (Banker et al., 984 annot generally be used for ranking DMUs, beause the effiieny sores of DMUs are ompared only with those related to the referene units. Andersen and Petersen (993 developed the super-effiieny ranking method for only effiient units. The methodology enables an extremely effiient unit o to ahieve an th effiieny sore greater than one by removing the o onstraint in the primal formulation. The dual formulation of the super-effiieny model omputes the distane between the Pareto frontiers evaluated without DMU o. Upon availability of the ranking results of super -effiieny method, all DMUs

3 20 International Symposium on OR and Its Appliations 2005 an be grouped into exlusive ategories (,,. Additionally, a set of n DMUs an be lassified into K homogeneous groups, eah of whih has n k DMUs with the same environmental harateristis ( k,, K. Eah group k generates responses I d,,, an take one of ategories. Let I k, I k, n k, and we assume ( kd n k n be the total number of lass DMUs of the k th group with DMUs. Then one an assume that n k, n k, p k pk 2,, pk, n k, follow a multinomial distribution for given probability,. The p represents the probability that a randomly seleted DMU within the kth group is ategorized as level. That is n or g ( p, p,, p : n k, nk2,, nk, pk, pk2,, pk, ~ MND k k 2 k, ( nk! n ( n, n,, n p, p,, p p, where k, k k 2 k, (2 n! k k 2 n k nk + nk2 +,, + nk, and p. The marginal mean and variane are E ( n nk p and V ( n nk p( p environmental fators z k,, zk (,, respetively. Often these marginal mean and variane would vary over group mainly due to the assoiated with a partiular group k. We all this between luster variation. As both the mean and variane are the funtions of p, we use a umulative logit model for p against the linear model of P z k exp +. That is ( γ 0 + γ zk + + γ zk exp ( γ + γ z + + γ z, 0 k k where P is the umulative probability that the result of group k turns out to be less than or eual to level. γ 0 and γ denote interept and regression oeffiients of z k, respetively. When the p is of our interest, it an be obtained as follows: p P Pk,. In model (3, we impliitly assume that p is ompletely determined for a given z k. But it may not be neessarily true always. There ould be the remaining k (3

4 Ranking Effiieny in Data Envelopment Analysis 2 part of variation in p due to random error even with same environmental fators. We all this within luster variation. We introdue the following random effets model whih an aommodate suh variations. That is p (,, k,, pk, ~ Dir (4 where Dir represents a Dirihlet distribution: f ( p,, p k ( +,, + Γ k, p (5 Γ ( Here exp + exp is assumed to be ( γ 0 + γz k + + γ zk ( γ + γ z + + γ z 0 k k ( γ + γ z + + γ z exp 0, k k + exp( γ + γ z + + γ z. 0, k k (6 This is to reflet the ovariate effets on the distribution of p based on (3. hoie of Dirihlet distribution is due to the fat that it desribes well the distribution of the probability and its onjugate relationship to multinomial distribution. Subseuently, the expeted value and variane of p an be obtained as follows: E (, p (7 V ( p 2 + (8 As the atual performane data ( p k pk 2,, pk,, an be updated: n k,, n k, ( + n, n p k,, pk, nk,, nk, ~ Dir k, + k, are obs erved, the distribution for, (9

5 22 International Symposium on OR and Its Appliations 2005 with E and V ( p nk,, nk, ( p n,, n k ( + n (0 + nk k, + n ( + n k l l 2 + l n + n k kl +. ( Marginal density of n then an be derived as follows: g ( n With E Γ nk! n! Γ + nk ( n E( E( n p nk, 2 ( n n Γ ( + n Γ( and V( n V( E( n p + E( V( n p n + φ where φ k k k (4., (2 (3 From (4, the variane of marginal distribution an aommodate the extra variability at an amount of φ that ould not be aptured in (. Note that, if n k, then the variane of marginal distribution is eual to that of onditional

6 Ranking Effiieny in Data Envelopment Analysis 23 distribution. In order to estimate unknown parameters, distribution of n and unknown parameters, ( γ, γ,, maximizing the following likelihood funtion of parameters: ( γ0,, γ 0, γ,, γ :,, L n n r K K k K k (,, n g n k k, ( ( γ 0 and γ, we obtain the joint 0 γ, are obtained by f p,, p g n,, n p,, p dp dp. k k, k k, k k, MLEs (maximum likelihood estimator of unknown parameters annot be found in a losed form. Algorithms to find MLEs reuire guesses about the initial values of those parameters. We suggest the use of the following fixed effet model to provide initial guesses about ( γ, γ, 0, γ : L f where K (,, γ, γ,, γ : n,, n g ( n,, n p,, p, 0 0 K k k k, k k, (5 γ (6 p is defined as in (3. The resulting ( γ ~, γ~,, ~ initial values for MLEs. After obtaining MLEs ( γ, γˆ,, ˆ ˆ γ 0 γ an be used as the 0, inferenes on unknown parameters an be made evaluating the Fisher information matrix. This is used to find the standard error of eah estimator from the inverse of negative Hessian matrix onsisting of the seond degree of partial derivatives of the orresponding log likelihood funtion with respet to a set of ( γ, γˆ,, ˆ 2 χ distribution. ˆ γ 0. Then γˆ γ s. e ( γˆ 2 is known to follow a When the resulting MLEs ( γˆ 0, γˆ,, γˆ replae ( γ, γ,, γ and (4, one an obtain ˆ ( and ( E n new, the performane of a new group with V n new, 0 in (3 ˆ and they an be used to predit n new DMUs for given environmental 00 onfidene interval harateristis ( z, new,, z, new. Additionally, a ( % for the expeted performane of a new group, E ( n new,, an be approximately obtained as follows:

7 24 International Symposium on OR and Its Appliations 2005 exp( γˆ 0 + rz ˆ, new Z2 ˆ σ γˆ ˆ 0 + rz new, ( γˆ 0 rz ˆ new, Z2 ˆ σ γˆ 0 + rz ˆ new, ( γˆ 0, + rz ˆ, new Z2 ˆ σ γˆ + rz ˆ 0, new, ( γˆ 0, rz ˆ, new Z2 ˆ σ γˆ 0, + ˆ rz new, exp ( γˆ 0 + rz ˆ new, + Z2 ˆ σ γˆ ˆ 0 + rz new, ( γˆ 0 rz ˆ, new Z2 ˆ σ γˆ 0 + rz ˆ new, ( γˆ 0, + rz ˆ, new + Z2 ˆ σ γˆ + rz ˆ 0, new, ( γˆ 0, rz ˆ new, Z2 ˆ σ γˆ 0, + rz new, L nnew + exp + U exp + exp + n + exp + + new exp + exp + + ˆ (7-a (7-b where σˆ γˆ 0 + ˆrz new, 2 znew, V( rˆ + 2 ( znew, z +, newov( rˆ, rˆ znewnew, z, ov( ˆr, rˆ γˆ 0 z 0, new γ ˆ and. Here, L and U are, respetively, the lower and upper onfidene limits for E ( n new,. This kind of interval estimation an help omparison of the expeted performane among several different groups. 3 A ase Study In this setion, we apply the proposed approah to the empirial ase. In order to evaluate the relative effiienies of tehnology ommerialization projets in the area of information tehnology (IT, we utilize the data obtained from Korean Information Tehnology Transfer enter in 998. This overs 489 ommerialization projets ompleted during The uestionnaires regarding thirty one variables were sent to the representatives of tehnology transferee ompanies, and 3 out of the reeived uestionnaires were onsidered as DMUs after eliminating missing values and illogial responses. All thirty one variables were measured in 7 point Likert sale and had potential to be used as inputs or outputs for DEA. We used fator analysis to redue the dimension of these variables and ome up with a total of nine fators. Eah tehnology ommerialization projet was then evaluated in terms of six input and three output fators. Input fators used were the R&D ability of a tehnology provider, the tehnology reeiver s management ability, the tehnology,

8 Ranking Effiieny in Data Envelopment Analysis 25 reeiver s appliation ability of new tehnology, tehnology transfer enter fator, market ondition, and regulation fator. Output fators were tehnologial ommerialization suess, spreading expet effet, and tehnology improvement in the ompany. All these fators were taken from SEM (Strutural Euation Model of Sohn and Moon (2003 where the observed variables in the uestionnaires were used as omponents for latent variables of the onfirmatory fator analysis. Based on these input and output fators, we first used super -effiieny ranking analysis (Andersen and Petersen (993 to rank 3 ommerialization projets (DMUs and ategorized them into the three lusters: highly reommended group, in-between group and failed group. onsidering the proportion of DMUs in eah ategory as similarly as possible, DMUs with effiieny sore higher than.0 are ategorized as highly reommended, DMUs with effiieny sores less than 0.8 as failed ones, otherwise undeided ones. Support for the DMUs of undeided luster is ontingent and depends on the resoures available. We then relate the group membership of eah DMU with related group harateristis representing the type of tehnology, tehnology provider and its reeiver using the proposed model (3. The following dummy variables are used for eah grouping of environmental harateristis: i. Tehnology harateristi of tehnology field - Teleommuniation: ommuniation net, interhange, fa simile ( z - Information : omputer, S/W, Interfae ( z 2 - Eletri & broadasting ( z 3 - Semiondutor/(mahine parts (Referene group harateristi of produt - Information and ommuniation servie ( z 2 - System and finished produt ( z 22 - (mahine Parts ( z 23 - S/W ( z 24 - Et. (Referene group Projet Type - Government-run projet ( z 3 - Other projet (Referene group Appliation - Existing business ( z 4 - New business (Referene group Tehnology level - opying level ( z 5 - Absorption level ( z 52

9 26 International Symposium on OR and Its Appliations 2005 ii. - Improvement level ( z 53 - Innovation level (Referene group Tehnology provider onsortium - Joint researh ( z 6 - Independent researh (Referene group Institution - orporation ( z 7 - Researh institute or university (Referene group iii. Tehnology reeiver ompany Size - 00 or more employees ( z 8 - Less than 00 employees (Referene group R&D expenditure ratio - 2.5% or more R&D expenditure ratio ( z 9 - Less than 2.5% (Referene group These riteria an be onsidered as the environmental fators of DMU. Details of the levels of eah environmental harateristi are given in Figure. Note that, the underlined level of eah grouping riterion represents the referene group for the linear model in (3. Figure. Grouping riteria of tehnology ommerialization projets

10 Ranking Effiieny in Data Envelopment Analysis 27 All possible ombinations of the levels of theses environmental harateristis are apparently 09, where we have a total of 3 DMUs. Aording to this ombination, four groups have three members, 4 groups have two members and, the rest of them, 9 groups onsist of a single member. We apply this information to (5 where the nine kinds of ategorial variables z, z are used to represent the nine ombinations of environmental (, 9 harateristis. In order to estimate MLE, we first find the initial values, ~0,2,3 γ ~,,9, from the fixed effets model (6 based on γ ( and ( the information for n, n, and z ( k, 09 effets model are displayed in Table. k k. The results of the fixed Table. Results of the fixed effets model Parameter Estimates Standard hi-suare Pr > his Error p-value (Interept (Interept harateristis of produt (Information & ommuniation servie 2 (System & finished produt 3 (Mahine parts (S/W (Teleommuniation harateristis of 22 (Information field 23 (Eletroni & broadasting 3 (Projet type (Appliation type (opying level Tehnology 52 (Absorption level level 53 (Improvement level 6 (onsortium (Institution

11 28 International Symposium on OR and Its Appliations (Numbers of employees (R&D expenditure ratio Next, we applied the Newton-Raphson method available in SAS PRO NLP γ ~, γ ~,, γ~. However, it (SAS Institute, 998 to find the MLEs based on ( failed to onverge. This might be due to a highly nonlinear struture of our likelihood funtion and in an effort to redue the dimension of parameter spae, we only inluded in the linear model those whih turn out to be signifiant in the fixed effets logisti regression. For this purpose, hi-suare test is performed at 0% level of signifiane using the p-values given in Table. As a result, three signifiant ovariates are seleted: harateristis of produt, projet type, and onsortium type of projet. Aording to these three riteria, 3 DMUs an be lustered into twenty groups as displayed in Table 2. Table 2. Regrouping the 3 DMUs in terms of three environmental harateristis harateristis of Tehnology ombination Group Number of high ly Number of Number of undeided rejeted reommended DMUs in a DMUs in a DMUs in a group group group Governmentrun projet Joint researh GR 0 Information & Government- projet researh Independent ommuniationrun GR servie Other projet Joint researh GR 3 0 Other projet Independent researh GR Governmentrun projet Joint researh GR System & Governmentrun projet researh Independent finished GR produt Other projet Joint researh GR Other projet Independent researh GR Governmentrun projet Joint researh GR 9 2 Governmentrun projet researh Independent Mahine parts GR Other projet Joint researh GR Other projet Independent researh GR S/W Governmentrun projet Joint researh GR Governmentrun projet researh Independent GR

12 Ranking Effiieny in Data Envelopment Analysis 29 Et Other projet Joint researh GR Other projet Independent researh GR 6 2 Governmentrun projet Joint researh GR Governmentrun projet researh Independent GR 8 Other projet Joint researh GR Other projet Independent researh GR After regrouping, we ~ fit again the fixed effets logisti regression and the, γ~, γ~, γ ~, are set to be the initial values for estimated parameters, ( γ ( 0, γ, γ 3, γ 6 ( ˆ, γˆ, γˆ, γ γ as in Table 3. We then obtain the maximum likelihood estimators, γ 0 ˆ 3 6, using (3 and the resulting parameter estimates as well as their standard errors are also displayed in Table 3. Table 3. ML estimates for the random effets model Parameter Initial Model based Standard hi-suare p-value Estimates Estimates Error γ (Interept ˆ0 ˆ γ (Interept γ ˆ (Information & ommuniation servie γ ˆ2 (System & (harateristis offinished produt produt γ ˆ3 (Mahine parts γ ˆ4 (S/W Referene group (Et produts γ 3ˆ (Government-run (Projet type projet Referene group (Other projet γ (Joint researh (onsortium 6ˆ Referene group (Independent researh Aording to the results in Table 3, all parameters in three ovariates are signifiant at 0% level. This would indiate that the harateristi of produt, projet type, and onsortium type are the important environmental fators that an be used to predit the effiieny of ommerialization senarios. In terms of the

13 30 International Symposium on OR and Its Appliations 2005 harateristis of produt, most of ommerialization projets tend to have lower ranks than the other types of IT produt suh as multimedia ontents, seurity produt, and A/S servie. These results may be assoiated with the fat that these areas reently stand a spotlight in IT industry due to the rapid development of internet servie, networking, and produt liability, respetively. As for the projet type, the government-run projets tend to have higher ranks than the other types of projets. In an effort to esape from the finanial risis in 998, Korean government has made a ontinuous investment on the ommerialization of new tehnology in the filed of IT industry. As a result, government-run projets have had strong momentum whih in turn indued the remarkable improvement on the effiieny of ommerialization. Similarly, the result for the onsortium type shows that the ommerialization projets in a form of the joint researh have higher ranks than those of the independent researh institution. It is onerned with that many ompanies perform projet as a form of onsortium in order to not only ahieve higher performane but also maintain lower risk. Using euations (4, (7, (8, (9, (0, and (, we an obtain the onditional mean and variane of the number of highly reommended DMUs in eah group. All of these results are displayed in Table 4. The results in Table 4 show that mean varies over different tehnology groups due to the environmental fators to whih they are exposed. As referred to in this paper, it is alled between luster variation. At the same time, the DEA effiienies in eah group vary due to the random error following beta distribution. We all this within luster variation. From the varying variane, one an see that this is not onstant over individual lusters. The results show also that the posterior means of about half of all twenty tehnology groups (GR 2, GR 3, GR 4, GR 8, GR 9, GR 3, GR 8, GR 9, and GR 20 beame higher than prior ones while the rest of them are lower than prior ones. However, all the posterior onditional varianes are lower than the prior random effets. When we ompare the results in Table 4 with the sample means, whih onsiders no environmental fators in Table 2, we find that the resultant posterior distribution reflets the degree of onformity of the observed data to the prior distribution for the effiieny. For example, it is shown that all the DMUs in GR 20 are highly reommdended ones without onsidering any environmental fators. However, it is expeted that only about 87% of DMUs would be highly reommended ones aording to the result of our random effets model. On the other hand, GR, GR 6, and GR 0 have no highly reommended DMUs from the super -effiieny method while it turns out from random effets analysis that there would exist about 5%, %, and 0.8% highly reommended ones in these three groups, respetively. When unknown parameters are replaed with MLEs in (0, fitted model an be used to obtain the preditive distribution for the number of highly reommended DMUs of new tehnology group at the seletion stage of several alternatives. At this stage, there would be no observed inputs and outputs exept for the tehnology senarios in terms of the grouping riteria.

14 Ranking Effiieny in Data Envelopment Analysis 3 In order to illustrate this, we use the seven test data, eah of whih ontains five DMUs. These test data were originally reported by Sohn and Moon (2003 and were desribed in terms of the nine grouping riteria. We onsider them as our senarios. However, note that only the three of the nine ovariates turned out to be signifiant through our analysis. Thus, we obtain the preditive distribution by using these three ovariates. The preditive mean and variane, and 95% onfidene interval for eah tehnology group are obtained using (, (2, (4 and are reported in Table 5. In general, the expeted number of highly reommended DMUs in all seven tehnology senarios exeeds the /3 of the samples. Among the seven different kinds of tehnology senarios, GR E turns out to have the highest potential On the other hand, GR A and GR B are expeted to be the least effetive senarios ( These results an be applied to selet the potentially effetive tehnology ommerialization map among several alternatives at the planning stage of new tehnology development. It is interesting to note that all of the 95% onfidene intervals for the effiieny of senarios are overlapping exept for that for GR E. This is mainly due to the inflated variane of the transformed ML estimates for ovariate parameters. We ompare these results with Sohn and hoi (2005 that ategorized the tehnology senarios into effiient and ineffiient ones by adopting beta distribution for the random effets for the R based DEA. Major differene between the two results is as follows: there were no effiient groups in Sohn and hoi (2005 whereas all DMUs turn out to be the highly reommended groups by having 95% E exeeding /3 of the sample DMUs. Suh onfidene intervals for ( n new, ontraditive results are mainly due to the fat that system and finished produt turns out to be signifiantly meaningful in the ranking analysis while not in the effiieny analysis. For more effetive omparison, Table 6 shows the most freuent level of eah environmental fator for the tehnology senarios whih are ategorized into failed and undeided ones in ranking analysis. Note that all of these groups turned out to be ineffiient ones in R effiieny analysis (Sohna and hoi As an be seen in Table 6, the ommerialization projets for system and finished projets in the form of non-governmental projets transferred to the ompany with more than 00 employees have higher ranks than those for mahine parts in the form of governmental projets transferred to the ompany with less than 00 employees. Table 6. Most freuent level of eah environmental fator for rejeted and undeided DMUs Rejeted DMUs Undeided DMUs harateristi of produt Mahine parts System and finished produt harateristi of tehnologyteleommuniation: Teleommuniation: field ommuniation net, interhange, ommuniation net, interhange, fasimile fasimile Projet Type Government-run projet Other projet Appliation New business New business

15 32 International Symposium on OR and Its Appliations 2005 onsortium Independent researh Independent researh Institution orporation orporation ompany Size Less than 00 employees 00 or more employees R&D expenditure ratio R&D 2.5% or more R&D 2.5% or more Tehnology level opying Tehnology Level opying Tehnology Level 4 onlusions In this paper, we proposed a multinomial Dirihlet regression model whih an be used for the purpose of seletion of new projets. A ase study was presented in the ontext of ranking analysis of information tehnology ommerialization projets. We showed that our approah an omplement the DEA ranking results with environmental fators and at the same time it an failitate the predition of effiieny of new DMUs with only given environmental harateristis. We illustrated both the effiieny-based ranking analysis on 3 IT tehnology senarios and the predition of the number of highly reommended DMUs for the given senarios with six inputs, three outputs, and nine tehnology grouping riteria onsidered as ovariates. Aording to our empirial result, tehnology, tehnology provider, and tehnology reeiver have at least one influential environmental fator that plays signifiant roles in terms of ranking predition. However, there are some other fators that are potentially important but were not inluded in our study as the harateristis of tehnology, tehnology provider, and tehnology reeiver. They are internal fators suh as the ulture of ompany, the struture of ompensation for ommerialization suess, the inlination of the ompany s EO, and so on. They an be aommodated in the future survey. Although the proposed approah an be effetively utilized to inorporate the environmental fators with the DEA results, it has also some limitations to be further onsidered. One of them is related to the diffiulty in onsidering all possible fators due to the highly nonlinear struture of the likelihood funtion. Another problem is assoiated with the effetive way to set initial values for MLEs. Another expansion would be the hoie of K, the number of groups. As an be seen from our empirial implementation, there ould be many different ways to determine K (Green and Hensher, They are left for further areas of researh. In summary, the proposed approah an be widely appliable to a large family of real-world problems. They would be espeially benefiial to the deision making proess in resoure management problems where some auxiliary harateristis of the organizations are available. Referenes Anderson, P., and Peterson, N A proedure for ranking effiient units in data envelopment analysis. Management Siene 39( Banker, R. D., harnes, A., and ooper, W. W Some models for estimating tehnial and sale effiieny in data envelopment analysis. Management Siene

16 Ranking Effiieny in Data Envelopment Analysis 33 harnes, A., ooper, W. W., and Rhodes, H Measuring the effiieny of deision making units. European Journal of Operational Researh harnes, A., ooper, W. W., Lewin, A. Y., and Seiford, L. M Data Envelopment Analysis: Theory, Methodology, and Appliation. Kluwer Aademi Publisher. London. ooper, W. W. and Tone, K Measures of ineffiieny in data envelopment analysis and stohasti frontier estimation. European Journal of Operational Researh Farrell, M. J. 95. The measurement of produtive effiieny. Journal of Royal Statistial Soiety Series A Fernández,., Koop, G. and Steel M A Bayesian analysis of multiple-output prodution frontiers. Journal of Eonometris 98 ( Fernández,., Osiewalski, J. and Mark F. J. Steel On the use of panel data in stohasti frontier models with improper priors. Journal of Eonometris 79 ( Fridman, L. and Sinuany-Stern, Z ombining ranking sales and seleting variables in the data envelopment analysis ontext: The ase of industrial branhes. omputers and Operations Reserarh 25( Green, W. H., Hensher, D. A A latent lass model for disrete hoie analysis: ontrast with mixed logit. Transportation Researh Part B Kohers, T., Huang, M and Kohers, M Market pereption of effiieny in bank holding ompany mergers: the roles of the DEA and SFA models in apturing merger potential. Review of Finanial Eonomis 9 ( Koop, G., Osiewalski, J. and Mark F. J. Steel Bayesian effiieny analysis through individual effets: Hospital ost frontiers. Journal of Eonometris 76 ( Korea National Statistial Offie Major statistis of Korean eonomy, Researh Report, Seoul, Korea. Kumar, V. and Jain, P. K ommerialization of new tehnologies in India: an empirial study of pereptions of tehnology institutions. Tehnovation Lovell,. A. Knox, Reinhard, S. and Thijssen, G. J Environmental effiieny with multiple environmentally detrimental variables; estimated with SFA and DEA. European Journal of Operational Researh 2 ( Seiford, L. M. and Thrall, R. M Reent development in DEA: the mathematial programming approah to frontier analysis, Journal of Eonomis SAS Institute SAS/STAT User s Guide 6.03: SAS Institute, ary, N. Sengupta, J. K Dynamis of data envelopment analysis: theory of systems effiieny. Kluwert Aademi Publishers. London. Sohn, S. Y A omparative study of four estimators for analyzing the random event rate of the Poisson proess. Journal of the Statistial omputing and Simulation Sohn S. Y Empirial Bayesian analysis for traffi intensity: M/M/ ueues with ovariates. ueueing Systems

17 34 International Symposium on OR and Its Appliations 2005 Sohn, S. Y Bayesian dynami foreasting for attribute reliability. omputers and Industrial Engineering 33( Sohn. S. Y Robust parameter design for integrated iruit fabriation proedure with respet to ategorial harateristi. Reliability Engineering and System Safety Sohn, S. Y Robust design of server apability in M/M/ ueues with both partly random arrival and servie rates. omputers and Operations Researh Sohn, S. Y. and Moon, T. H Strutural euation model for prediting tehnology ommerialization suess index. Tehnologial Foreasting & Soial hange Sohn, S.Y., Yoon, K. B., Jang, I. S., 2005, Random Effets model for the reliability management of modules of a fighter airraft. Aepted to Reliability Engineering and System Safety. Sohn, S.Y., Yoon, K. B., 2005, Dynami preventive maintenane sheduling of the modules of fighter airrafts based on random effets regression model. submitted for publiation, Sohn, S. Y. and hoi, H Random Effets Logisti Regression Model for Data Envelopment Analysis with orrelated Deision Making Units. JORS, aepted Tsionas, E. G ombining DEA and stohasti frontier models: An empirial Bayes approah, European Journal of Operational Researh, West, M. and Harrison, J Bayesian foreasting and dynami models. Springer-Verlag. NY.

18 Table 4. Random effets & onditioanl means and varianes of effiieny of twenty tehnology groups Highly Random effet reommended distribution Highly reommended onditional distribution Highly reommended DMUs Dir DMUs Dir (, 2, 3 ( ', ' 2, ' 3 DMUs Groups Sample means Prior 2 3 Prior mean ' ' 2 3 variane Posterior Posterior mean variane GR GR GR GR GR GR GR GR GR GR GR GR GR GR GR GR GR GR GR GR Ranking Effiieny in Data Envelopment Analysis 35

19 Group GR A GR B GR GR D Table 5. Preditive mean, variane, and 95%.I. for the performane of the seven tehnology senarios Tehnology Senario Information and ommuniation servie Teleommuniation: ommuniation net, interhange, fasimile Government-run projet Existing business Innovation tehnology level Independent researh orporation Less than 00 employees R&D 2.5% or more Information and ommuniation servie Teleommuniation: ommuniation net, interhange, fasimile Government-run projet New business Innovation tehnology level Independent researh orporation Less than 00 employees R&D 2.5% or more System and finished produt Teleommuniation: ommuniation net, interhange, fasimile Government-run projet New business Improvement tehnology level Independent researh orporation 00 or more employees R&D 2.5% or more System and finished produt Teleommuniation: ommuniation net, interhange, fasimile Government-run projet New business Sample Highly reommended DMUs size E ( n new, ( n new, V 95%.I [ , ] [ , ] [ ,3.0466] [ ,3.0466] 36 International Symposium on OR and Its Appliations 2005

20 GR E GR F GR G Improvement tehnology level Independent researh orporation 00 or more employees R&D Less then 2.5% System and finished produt Teleommuniation: ommuniation net, interhange, fasimile Other projet Existing business Absorption tehnology level Joint researh orporation 00 or more employees R&D 2.5% or more System and finished produt Semiondutor / (mahineparts Government-run projet New business Absorption tehnology level Independent researh Researh institute or University Less than 00 employees R&D 2.5% or more Software Information: omputer, S/w, Interfae Government-run projet Existing business opying Tehnology Level Independent researh Researh institute or University Less than 00 employees R&D 2.5% or more [ ,3.8585] [ ,3.0466] [ , ] Ranking Effiieny in Data Envelopment Analysis 37