Comparison of a Data Imputation Structural Equation Modeling Accuracy Estimation Between Constrained and Unconstrained Approaches

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1 0 Intnatonal Confence on Informaton and Electroncs Engneng IPCSIT vol.6 (0) (0) IACSIT Press, Sngapore Comparson of a Data Imputaton Structural Equaton ng Accuracy Estmaton Between Constraned and Unconstraned Approaches Narong Photh and Somcha Prakancharoen + Faculty of Informaton Technology, Kng Mongkut s Unvsty of Technology North Bangkok, Thaland. Faculty of Appled Scence, Kng Mongkut s Unvsty of Technology North Bangkok, Thaland. Abstract. Ths study amed to comparson of a data mputaton structural equaton modelng (SEM) accuracy estmaton between constraned and unconstraned approaches. The measurement accuracy of the model based on the mean magntude of relatve ror (MMRE) model. The model s developed by usng the onlne database from Unvsty of Calforna, Irvne (UCI) whch s a data set on waveform genators. Indcators (,00 sets) methods we as follows: ) Data set was dvded nto two groups (expmental group of,000 sets and test group of 00 sets); ) The expmental group was analyzed by three man factors (F,, F3); 3) Create a SEM; 4) The remanng ndcators from the results n secton 3 we used to create new factors wth the constraned approach. All the ndcators are related and used to construct a SEM to estmate the equaton mssng. The test data was substtuted n the equaton to fnd the accuracy whch was 43.00% (MMRE was 57.00%); 5) the remanng ndcators from the results n secton 3 we used to create a new factor wth the unconstraned approach. The test data was also substtuted n the equaton to fnd the accuracy whch was 65.7% (MMRE was 34.9%). Thus, comparng estmates of mssng data showed that usng the SEM wth the unconstraned approach employed ndcators, whch we related for more accuracy whle MMRE declned usng the constraned approach wth related ndcators. Keywords: Data Imputaton Estmaton, Structural Equaton ng (SEM), Constraned Approaches, Unconstraned Approaches.. Introducton.. Background Genal research nformaton n ths area s requred to complete the analyss n ord to acheve the most accurate and precse results. Howev, some data may be mssng or ncomplete. Thefore, n ord to brng a data set that s complete and ready to use. Some data wll be mssng. Ths would result n the records becomng redundant or obsolete, thus analyss and forecast of data s needed. If some of the data set we mssng n large amounts, data that s needed should avod devaton, whch would lead to ror of the results and need to be obtaned through processng. The estmaton of mssng data wll help n preparng data to replace the mssng research data sets. From the research on estmaton of loss of data, such as research Prakancharoen [] usng SEM to estmate the tme to develop applcaton software orented network, also researchs Photh and Prakancharoen [] usng SEM between wth dscrmnant analyss and wthout dscrmnant analyss for accuracy comparson of mputaton methods, and research Rufus [3] usng solutons for mssng data n SEM for new data all use smlar approaches to solve ths ssue. In ths study, researchs comparson of a data mputaton SEM accuracy estmaton between constraned and unconstraned approaches. The research nformaton s taken from the onlne database, UCI Machne Learnng Repostory s a collecton of waveform database genator data sets (,00 sets). The measurement accuracy of the estmated loss from the MMRE was found to be hghly accurate... The purpose of the research To estmate mssng data by usng product ndcator approaches of SEM wth the constraned approach. + Correspondng author. Tel.: ; fax: E-mal address: narong@sueksa.go.th, spk@kmutnb.ac.th 45

2 To estmate mssng data by usng product ndcator approaches of SEM wth the unconstraned approach. To compare the accuracy of estmates the mssng data by SEM, product ndcator approaches (PIA) of SEM wth the constraned approach and PIA of SEM wth the unconstraned approach..3. Scope of research The data used n ths opaton was a waveform database genator data set from the onlne database, and UCI Machne Learnng Repostory as a data type wth,00 sets, whch we dvded nto two groups: expmental group (000 sets) and test group (00 sets). The data set has ndcators, namely, V-V and C classes for the descrpton of each ndcator V., whch can be vewed at detmned that the ffth ndcators () n the equaton of the test group we mssng valuable data used to compare the accuracy of the estmaton method. Mssng value due to a measure of ths needs to fnd the best relatonshp assocated wth oth ndcators n a waveform database genator data set.. Theory and Methodology.. Factor Analyss Factor Analyss [4] s a technque used to extract the factors (component) from a group of ndcators that are related to each factor. Ths wll be used nstead of a group of ndcators that have the same group. Ths s a technque that reduces the numb of dmensons or manfest varable and consds the sutablty of the extracted factors. By checkng the statstcs Kas-Mey-Olkn: KMO (KMO>0.60) factors obtaned wll only valdate the consded values. Able to explan the varablty of all the factors togeth (total varance explaned) wth the nvse of each varable wth no apparent extracton factor would greatly beneft ths approach. If the value of a hgh pcentage (cumulatve explaned varance) showed that the factors can represent a good ndcator, ths can be formulated as follows. F = wx+ wx wpxp + e () whe F =factor, w =coeffcent of varable x, x =manfest varable and e =margn of ror... Structural Equaton ng (SEM) SEM [], [5] s a technque used to analyze the relatonshp of factors from the survey (exploratory) wth a key and then extract a model of the relatonshp of varous factors, whch s the man theory or hypothess of ths study. From the statstcs of ) Ch-square ( χ ) should be a non-sgnfcance (P>0.05) ) Goodness of Ft Index (GFI>0.90) 3) Root Mean Square Error of Approxmaton (RMSEA<0.06) and 4) Hoelt's N, the value (Hoelt's. N>75) s used to check the adequacy and approprateness of sample sze (case) n SEM..3. Product Indcator Approaches of Structural Equaton ng (PIA of SEM) PIA of SEM [6] s a technque used to estmate the stablty of the equaton appears n the relatonshp between varables. The equaton s made up of ndcators that are related, formulated as follows. XZ = λλξξ + λξ δ + λ ξ δ + δδ () whe X =predctor of varable, Z =modator of varable, ξ =factor, λ =factor loadng and δ =margn of ror. To buld PIA wth two dffent technques. ) Constraned approach [7] creates a new factor XZ by brngng a measure of the factor X by match multpled wth all ndcators of factor Z and repeated untl completed. ) Unconstraned approach [8] creates a new factor XZ by brngng a measure of the man to multply ndcator : match wth a measure of factor Z..4. Accuracy Evaluaton Crton Accuracy Evaluaton Crton [] of a new data set, whch must be precsely compatble (model best ft) by applyng a set of new data (predcted mssng) dved from the estmaton of mssng data to vfy the real data set (actual mssng) and then calculate the Magntude of Relatve Error (MRE) accordng to the formula. X 46

3 ActualMssng - PredctedMssng MRE = (3) ActualMssng The mssng data ( =,,..., n) must be used for calculatng the Mean Magntude of Relatve Error (MMRE). If t s found that the results of MMRE have small values, the results should be precse or vy close to the real data as formulated below. 3. Methodology MMRE ActualMssng - PredctedMssng n = x00 (4) n = ActualMssng Accuracy = 00 - MMRE (5) 3.. fcaton of data sets for the research fcaton or dvded data set of waveform database genator,00 sets nto two groups: the expmental group was,000 data sets and the test group was 00 data sets. 3.. The factor analyss of expmental group The expmental group focused on the factor analyss method by prncpal component analyss to provde a measure that s relevant to the factors n the same way as rotaton varmax to reduce the numb of ponts. Ths should measure the weght of each factor to as low as possble. Results from the analyss of new factors wth KMO we 0.96, and new factors from extracton consst of three man factors F, and F3 are shown n Table. Table : Results of man factors and ndcators Factor F F3 Indcator of Factor V7, V9, V0, V6,, V8, V8, V9, V0,, V, V6, V7,,, V,, V V, V 3.3. Structural Equaton ng The man factors F, and F3 of buldng a SEM are shown n Fg.. The model approprate to revew the statstcs of the compatblty of the model to goodness of ft: RMSEA, GFI and Hoelt's N whch are the adequacy of the sample cases. The results n Table and the new SEM are shown n Fg.. V9 V0 V7 e9 e0 e7 C V6 e6 C F.75 V8 V8 e8 e8 V9 e V0 e0.48 F3 V V e e F V0 V9 V8 V7 V9 V V6 V V7 V V e6 e e7 e e e0 e9 e8 e7 e9 e Fg. : Prototype of SEM Fg. : SEM standardzed type Table : The statstc s compatblty of SEM χ P GFI RMSEA Hoelt s N Default / Product ndcator approaches of structural equaton modelng wth constraned approach 47

4 The only measure left ov from the results of the SEM accordng to Fg. s F = {V9, V7, V8, V9, V0} and = {V,,,, } to create new factors related. By brngng a measure of the factor F one by one to match multpled wth a measure of factor all and repeats untl all ndcators of the factors F. A result s F = {V7V, V7, V7, V7, V7, V8V, V8, V8, V8, V8, V9V, V9, V9, V9, V9, V0V, V0, V0, V0, V0} and then create SEM have the statstcs of compatblty n Table 3, and the new SEM s depcted n Fg. 3 wth the equaton estmated by equaton 6-9. C V8V V9V.4 F V0V.53 Fg. 3: The constraned approach model standardzed type Table 3: The statstc s compatblty of the constraned approach model χ P GFI RMSEA Hoelt s N Default /344 = (0*C)+ (6) = (+(0.9*F))/(-0.98) (7) F = (0.83*V8V)+(0.66*V9V)+(0.4*V0V) (8) = (-((0.53*)+(0*)-(0.79*)))/(0.8) (9) 3.5. Product ndcator approaches of structural equaton modelng wth unconstraned approach The only measure left ov from the results of the SEM accordng to Fg. s F = {V9, V7, V8, V9, V0} and = {V,,,, } to create new factors related. By applyng a metrc from the factor F to multply : match wth a measure of the factors. A result s F = {V9, V7, V8, V9, V0V}, and then create SEM have the statstcs togeth n Table 4, and the new SEM as Fg. 4 wth the equaton estmated by equaton 0-3. C V8.44 F.8 V Fg. 4: The unconstraned approach model standardzed type 48

5 Table 4: The statstc s compatblty of the unconstraned approach model χ P GFI RMSEA Hoelt s N Default /365 = (0.89*C)+ (0) = (+(0.66*F))/(-0.75) () F = (0.44*V8)+(0.8*V9) () = (+(0.8*))/(0.8) (3) 4. Results The test group of 00 sets was assgned to fnd mssng and estmate the replacement value of mssng data as follows: ) the data mputaton estmaton methods usng PIA of SEM wth the constraned approach as equaton 6-9, the result of accuracy was 43.00% (MMRE was 57.00%) and ) the data mputaton estmaton methods usng PIA of SEM wth the unconstraned approach as equaton 0-3, The result of accuracy was 65.7% (MMRE was 34.9%). Thus, comparng estmates of mssng data showed that usng the SEM wth the unconstraned approach and related ndcators had hgh accuracy, whle MMRE declned usng the constraned approach wth related ndcators. 5. Conclusons Data mputaton estmaton methods usng PIA of SEM wth a data set from the waveform database genator. Numc ndcators of,00 sets of nonlnear type showed that the groupng of data sets or analyss of man factors for the ndcators are related to factors n the same area. When estmatng mssng data, the results of MMRE rors we reduced. Makng a new data from the mssng estmaton method s more accurate than the new values. Suggestons about the data mputaton estmaton methods usng PIA. The related ndcators are used n the case of latent factors outsde the relatonshp between the two drectons only. If no such event, ths method wll not be able to be used. 6. Refences [] Prakancharoen S. The estmated tme to develop applcaton software orented network Usng structural equaton modelng. Informaton Technology Journal. Year 4 Vol. 7. Bangkok: Kng Mongkut's Unvsty of Technology North Bangkok, 008. [] Photh N. and Prakancharoen S. "Accuracy Comparson of Imputaton Methods Usng Structural Equaton ng Between Wth Dscrmnant Analyss and Wthout Dscrmnant Analyss". Confence on Scence and Technology No. 8. Pathum Than: Thammasat Unvsty Rangst Campus, 00. [3] Rufus L. C. Solutons for Mssng Data n Structural Equaton ng. Research & Practce n Assessment Vol., Issue March 006. [4] Vantbancha K. Multvarate Data Analyss. Vol.. Bangkok: Chulalongkorn Unvsty Book Cent, 007. [5] Garson G. D. Data Imputaton for Mssng Values. North Carolna State Unvsty, USA, 005. [6] Karn S., Chrstna W., Helfred M. Nonlnear Structural Equaton ng: Is Partal Least Squares an Altnatve?. Meetng of the Workng Group Structural Equaton ng. Bln, Gmany, February 6-7, 009. [7] Joreskog, K. G., & Yang, F. Nonlnear structural equaton models: The Kenny-Judd model wth ntacton effects. In G. Marcouldes & R. Schumack (Eds.), Advanced structural equaton modelng (pp ). Mahwah, NJ: Lawrence Erlbaum Assocates [8] Marsh, H. W., Wen, Z., & Hau, K. T. Structural equaton models of latent ntactons: Evaluaton of altnatve estmaton strateges and ndcator constructon. Psychologcal Methods, 9,