RESEARCH ARTICLE ON SELF-SELECTION BIASES IN ONLINE PRODUCT REVIEWS Nan Hu School of Busnss, Stvns Insttut of Tchnology, 1 Castl Pont Trrac, Hobokn, NJ 07030 U.S.A. {nhu4@stvns.du} Paul A. Pavlou Fox School of Busnss, Tmpl Unvrsty, 1801 N. Broad Strt, Phladlpha, PA 191 U.S.A. {pavlou@tmpl.du} J Zhang Collg of Busnss, Unvrsty of Txas, Arlngton, 701 S. Nddrman Drv, Arlngton, TX 76019 U.S.A. {jzhang@uta.du} Appndx A Th J-Shapd Dstrbuton of Onln Product Rvws A random sampl of product nformaton and thr corrspondng consumr rvws wr collctd from Amazon n 005 usng Amazon Wb Srvc (AWS for mor than 77,000 books, DVDs, and Vdos from Amazon (Tabl A1. Tabl A1. Dscrptv Statstcs for Amazon s Data Product Catgory Numbr of Products Numbr of Rvws Man of Rvws Books 3,878 967,075 4.0 DVDs 17,978,034,55 4.19 Vdos 8,983 1,48,99 3.99 Fgur A1 shows th dstrbuton of th avrag ratng for all books, DVDs, and vdos on Amazon.com. MIS Quartrly Vol. 41 No. Appndcs/Jun 017 A1
Hu t al./slf-slcton Bass n Onln Product Rvws 0.45 0.4 Prcntag 0.35 0.3 0.5 0. 0.15 0.1 0.05 0 1 1.5.5 3 3.5 4 4.5 5 1 1.5.5 3 3.5 4 4.5 5 1 1.5.5 3 3.5 4 4.5 5 Book DVD VHS A v ra g R a tn g (A ll Fgur A1. Th Dstrbuton of Onln Product Rvws for All Books, DVDs, and Vdos on Amazon.com To vrfy that th J-shapd dstrbuton dos not vary ovr tm, w splt all Amazon s rvws nto four ual groups (ntal stag, arly stag, lat stag, fnal stag 1 basd on thr posts. Th J-shapd dstrbuton prssts (Fgur A. Fgur A. Th Dstrbuton of Onln Product Rvws Ovr Tm Fgur A3 shows th dstrbuton of thr randomly slctd products n ach of th thr popular product catgors wth mor than,000 rvws. Th rsults show that ths products also hav a bmodal, asymmtrc, lft-skwd dstrbuton, thus confrmng that th obsrvd J-shapd dstrbuton s not du to th small numbr of product rvws. 1 Ths four stags and thr labls ar proposd n a rlatv sns. Spcfcally, th ntal stag rflcts th arlst stag th product was frst rlasd; th fnal stag s th latst prod. Th J-shapd pattrn stll holds rrspctv of prods and th absolut ag of th rvws. A MIS Quartrly Vol. 41 No. Appndcs/Jun 017
Hu t al./slf-slcton Bass n Onln Product Rvws Fgur A3. Th Dstrbuton of Onln Product Rvws for Books, DVDs, and Vdos wth n >,000 Rvws Fgur A4 prsnts th dstrbutons of onln product rvws for frwar on Download.com wth fwr than 0 rvws, whch follow a bmodal, J-shapd dstrbuton. Ths s a strong ndcaton that th dstrbuton s not normal. Also, to show that th J-shapd dstrbuton appls to products wth a dffrnt man ratng, Fgur A4 also shows th dstrbuton of products wth a man of 3.5-star (roughly n th mddl and 4-star (rght hand sd. Fgur A4. Dstrbuton of Onln Product Rvws of Frwar on Download.com (# 0 rvws Fgur A5 shows th bmodal dstrbuton of onln rvws for products wth a man star ratng of 3 and 4. 3 Fgur A5. Th Dstrbuton of Books, DVDs, and Vdos wth Man Ratng of Thr- or Four-Stars W calculatd th man of ach product s onln rvws basd on all obsrvatons. Snc th man can b dcmal numbr, such as 1. or.1, w usd th followng classfcaton: If th man of th onln product rvws was btwn 1 and 1.5, w classfd th product nto a group wth a man = 1; f th man was btwn 1.5 and, w classfd th product nto a group wth a man = 1.5, tc. W also trd to classfy products wth a man ratng around 1 (.g., btwn 0.9 and 1.1, nto a group wth man = 1, and th rsults wr vry smlar. 3 Bmodalty s not du to a truncatd dstrbuton snc consumrs cannot wrt rvws hghr than fv or lowr than on star. Graphc plots of th man of product ratngs othr than 3.0 or.5 stars rval that thr ar fwr consumrs wrtng a rvw wth a fv-star ratng than thos wrtng a rvw wth a four-star ratng. In thos cass, howvr, thr ar stll fwr consumrs wrtng a thr-star rvw. MIS Quartrly Vol. 41 No. Appndcs/Jun 017 A3
Hu t al./slf-slcton Bass n Onln Product Rvws Fgur A5 shows that as th man ratng ncrass, th U-shapd dstrbuton bcoms mor lft-skwd, thus turnng nto a J-shapd dstrbuton. Bsds th graphcal nspctons (Fgurs A1 A5, w formally tstd whthr th dstrbuton of onln product rvws s normal usng th Kolmogorov-Snrnov tst (Chakravart t al. 1967, whch xamns f a sampl coms from a normally dstrbutd populaton. 4 Ths tst at th ndvdual product lvl showd that narly all products do not follow a normal dstrbuton. To furthr tst f th dstrbuton of onln product rvws for ndvdual products s bmodal, th nonparamtrc DIP tst (Hartgan and Hartgan 1985 was usd. Th DIP tst s a masur of dpartur from unmodalty; th DIP statstc for a unmodal dstrbuton approachs zro, whl th DIP statstc of a bmodal dstrbuton approachs a postv constant. 5 W obtan th DIP statstcs usng R. 6 Th DIP tst show that 90.17% of products hav a dstrbuton of onln rvws that s nthr unmodal nor normal. Vrtually all products wth a man star ratng btwn 1.5 and 4 stars do not follow a unmodal dstrbuton. Evn most products wth a man star ratng around 5 stars do not follow a unmodal dstrbuton. To furthr stablsh th J-shapd dstrbuton, w tst th uadratc Euaton A1 (Andrson 1998 usng th followng modl: f = α + α s + α s + β x + ε j 0 j 1j j j j mj mj j [A1] whr f j s th numbr of product rvws wth scor, for tm j, s j = 0 {1,, 3, 4, 5] s rvw scor for product j, x mj ar othr varabls that mght nflunc th ratng of tm j, such as prc, man ratng and product catgory, and ε j s an rror trm. Th null hypothss to accpt th bmodal dstrbuton s gvn by H 0 : α 1 < 0 and α > 0. To account for potntal dffrncs n product charactrstcs and mans, w ran a fxd ffct modl by rgrssng th numbr of product rvws on th star ratng (numbr of stars. As a robustnss chck, w ran sparat rgrssons for dffrnt groups composd of products from th sam product catgory and wth smlar man ratng of product rvws, and w thn stmatd th man coffcnt across ths catgors. Th rsults ar ualtatvly th sam. Th rsults whn all products ar pulld togthr show a sgnfcant ngatv α 1 = 40.54 and a sgnfcant postv valu α = 9.09. Thrfor, th stmatd uadratc curv of [A1] s symmtrc n trms of th ratng s =., whch ls to th lft of th mdan pont of 3, mplyng that onln product rvws for vrtually all products collctd from Amazon wthn th rang of 1 5 star ratngs hav a J-shapd (lft skwd bmodal dstrbuton. As an addtonal robustnss chck, w ran ths J-shapd tst on ndvdual product lvl. Our rsults ndcat that 83.1% of books, 8.% of DVD, and 76.0% of VHS follow a J-shapd dstrbuton. 4 W also mployd th Cramr-von Mss (Thod 00 and th Andrson-Darlng (Stphns 1974 tsts wth smlar rsults. 5 Bsds DIP tst, othr nonparamtrc tsts of unmodalty ar avalabl, such as th xcss mass tst (Mullr and Sawtzk 1991, and th Slvrman (1981 tst. Th DIP and xcss mass tsts ar uvalnt n th on-dmnsonal cas as th xcss mass statstc s xactly twc th DIP statstc (Chng and Hall 1998. Howvr, th DIP tst s smplr and mor consrvatv (Chng and Hall 1998; Hndrson t al. 000. Thrfor, f th DIP tst shows a larg prcntag of onln product rvws to hav a bmodal dstrbuton, th othr tsts ar lkly to provd vn mor pronouncd rsults. 6 For mor nformaton on R, s http://www.r-projct.org. A4 MIS Quartrly Vol. 41 No. Appndcs/Jun 017
Hu t al./slf-slcton Bass n Onln Product Rvws Appndx B Lab Exprmnt on Slf-Slcton Bass n Onln Product Rvws W askd 18 subjcts to rvw four products (musc CD, mov DVD, Accss softwar, IS txtbook as wll as thr rvw, purchas ntntons, and purchas mportanc on a 1 5 scal. Ths products wr chosn to vary n trms of product catgory (musc, movs, softwar, txtbook, pror ownrshp, famlarty, mportanc, and prc lvl ($10 $50. For ach product, w assurd that th subjcts wr famlar wth ach product. Thy wr askd to har all twlv 30-scond clps of th musc CD, and thy wr also askd to watch mov Ttanc f thy dd not. Subjcts usd Accss as part of a rurd class assgnmnt, whl for thm th IS txtbook was a rurd class txtbook. Subjcts wr askd to rat th product and also rport whthr (1 thy had alrady ownd th product, ( th mportanc of th product to thm, and (3 thr ntnton and passon to rport a product rvw. Th purpos s to compar th dstrbuton of onln product rvws from almost all rspondnts n th lab xprmnt wth that of rvws on Amazon.com. Tabl B1 shows th numbr of rspondnts for ach product, and dscrptv statstcs of thr rsponss. Th rspons rat of ovr 9% shows that th products wr rvwd by almost all partcpants n our sampl, and nonrspons bas tsts showd that th nonrspondnts dd not dffr from th rspondnts. Tabl B1. Sampl Charactrstcs Product Numbr of Subjcts Numbr of Rvws on Amazon Pror Ownrshp (Prcntag Intnton to Rvw (Man STD Purchas Importanc (Man STD Musc CD 197 157 8%.03 (0.95.3 (0.99 Mov DVD 199 107 35%.5 (1.00.69 (1.16 Softwar 03 10 66%.18 (0.97.59 (1.06 Txtbook 01 13 83%.54 (1.03 3.67 (1.17 Amazon s and th xprmnt s man ratngs for ach of th four products ar ut dffrnt (Tabl B. Whl th musc CD and txtbook ar ratd hghr on Amazon (p <.001, th mov DVD s ratd hghr among th xprmnt s rspondnts; fnally, th man ratng for th Accss softwar s roughly th sam btwn Amazon and th xprmnt. Tabl B. Dffrncs n Man Star Ratngs of Product Rvws Survy Vrsus Amazon Product Fld Study Amazon Eualty Tst (p-valu Musc CD 3.5 3.90 0.0000 Mov DVD 4.09 3.56 0.0000 Accss Softwar 3.53 3.60 0.7931 IS Txtbook 3.51 4.79 0.0000 Bsds graphcal dffrncs (Fgurs 1 and, w spcfd a systm of uatons to solat th slf-slcton bass: Ratng = α 0 + α 1 Ownrshp + α Intnton + α 3 Importanc + G 3=1α ProductDummy + ε [B1] Intnton = β 0 + β 1 Ratng + β Ratng² + β 3 Importanc + G 3=1β ProductDummy + η [B] whr Ratng = Th rspondnt s star ratng on a fv-pont Lkrt-typ scal anchord btwn on star and fv stars. Ownrshp = Bnary varabl whthr th rsondnt alrady owns th product. Intnton = Th rspondnt s ntnton to wrt a product rvw at Amazon.com on a fv-pont scal. Importanc = Th rspondnt s assssmnt of how salnt th purchas s on a fv-pont scal. ProductDummy = Rprsnts th fxd ffcts du to potntal dffrncs across th thr catgors. In Euaton [B1], w usd Ownrshp as a proxy for acuston bas. Euaton [B1] summarzs th prdctors of th star ratng. Th utlty thory suggsts that pror ownrshp s xpctd to ncras th man ratng. In fact, th man ratng of subjcts who alrady ownd th product MIS Quartrly Vol. 41 No. Appndcs/Jun 017 A5
Hu t al./slf-slcton Bass n Onln Product Rvws was sgnfcantly hghr than thos who do not (p <.05 (Tabl B3. Purchas mportanc was controlld for ts postv ffct on th star ratng snc consumrs who prcv th purchas to b mportant ar mor lkly to b postvly prdsposd toward th product and to wrt a postv rvw. In Euaton [B1], ntnton to wrt a rvw was usd as a proxy for undrrportng bas. If consumrs ar mor lkly to wrt a rvw whn thy ar thr xtrmly satsfd or dssatsfd, Intnton s postvly corrlatd wth ExtrmStarRatng (a dummy varabl =1 whn consumrs lav a on-star or fv-star ratng and 0 othrws. Wald s tst n Tabl B4 basd on Euaton [B3] supports ths postv corrlaton (χ² = 40.98, p <.0001. W stmat Euaton [] n whch th subjcts ntnton to rport a rvw on Amazon s dtrmnd by th subjct s star ratng. Ratng and Ratng² ar ncludd to account for a potntal nonlnar ffct of th rspondnt s star ratng and hr ntntons to wrt a rvw. Tabl B3. Dffrncs n Star Ratngs of Onln Product Rvws Basd on Pror Ownrshp Pror Ownrshp No Ownrshp Dffrnc Product (man (man Sgn Dffrnc t-valu p-valu Musc CD 4.0 3.18 + 1.0 4.3600 <.0001 Mov DVD 4.6 4.00 + 0.6.000 0.09 Accss Softwar 3.64 3.30 + 0.34.8600 0.0047 IS Txtbook 3.58 3.0 + 0.38.8700 0.0046 Tabl B4. Lklhood of Wrtng an Extrm Product Rvw Coffcnt Wald Ch-Suar p-valu Intrcpt -3.68 105.4 <.0001 Intnton 0.68 40.98 <.0001 DVD Dummy 1.31 0.74 <.0001 Softwar Dummy -0.04 0.01 0.9081 Txtbook Dummy -1.13 7.90 0.0050 Snc th Intnton varabl n Euaton [B1] s a lnar combnaton of othr varabls n Euaton [B], w adoptd th lmtd-nformaton maxmum lklhood (LIML stmaton to smultanously stmat th systm of uatons for acuston bas and undrrportng bas. 7 Th rsults ar rportd n Tabl B5. 8 4 ExtrmStarRatng = γ 0 = γ 1 Intnton + γ ProductDummy + ε [B3] = 7 Asymptotcally, SLS and LIML stmators hav th sam dstrbuton (Andrson 005. Evn though t s asr to comput SLS, LIML was usd bcaus (1 th paramtr stmaton mthod of smultanous uaton modls was basd on ML that s commonly blvd to yld supror stmators (Andrson 005; ( LIML taks nto account th covarancs of th rror trms; (3 SLS stmator trats th componnts of β asymmtrcally, whch runs contrary to smultanous uatons (Andrson 005, p. 9. 8 As a robustnss chck, bsds stmatng th systm of Euatons 1 and, w also stmatd ths uatons ndpndntly usng both OLS and logstc rgrsson. Furthrmor, w stmatd Euaton wth th sampl composd of all rspondnts, or thos rspondnts who alrady ownd th product bfor. All of ths tsts hav ualtatvly th sam rsults. A6 MIS Quartrly Vol. 41 No. Appndcs/Jun 017
Hu t al./slf-slcton Bass n Onln Product Rvws Tabl B5. Acuston Bas and Undrrportng Bas Basd on Systm Euatons [1] and [] Acuston Bas Undrrportng Bas Varabl Paramtr α Varabl Paramtr β Intrcpt.3*** Intrcpt 1.10*** Pror Ownrshp 0.13** Ratng -0.19* Intnton to Wrt Rvw 0.05 Ratng² 0.04** Purchas Importanc 0.8*** Purchas Importanc 0.44*** CD_Dummy 0.8*** CD_Dummy 0.13* DVD_Dummy 0.94*** DVD_Dummy 0.07 Softwar_Dummy 0.37*** Softwar_Dummy 0.11 N 800 N 800 Adjustd R² 8.9% Adjustd R² 9.9% DW 1.98 DW.07 ***p < 0.001; **p < 0.05; *p < 0.10 For acuston bas, aftr controllng for purchas mportanc, pror ownrshp (α 1 = 0.13, p < 0.05 was postvly lnkd to ratng, and ntnton to rport a rvw was not sgnfcant (α 3 = 0.05, p > 0.10. For undrrportng bas, th ngatv coffcnt of Ratng was margnally sgnfcant (β 1 = 0.19, p < 0.10, and th Ratng² coffcnt (β = 0.04, p < 0.05 was postv and sgnfcant. That mpls that consumrs ar mor lkly to wrt a rvw whn thy ar thr satsfd or dssatsfd, whl thy ar th last lkly to rport a rvw whn thr star β ratng s modrat ( β = 4. stars accordng to Euaton [B]. Ths rsults rnforc that acuston bas (rflctd through pror 1 ownrshp and undrrportng bas (rflctd through hghr ntntons to wrt a product rvw rsult n th obsrvd J-shapd dstrbuton. Fgur B1 shows that thr s a stark contrast btwn th mans of Amazon s onln product rvws and thos of th lab xprmnt rvws for th xact sam four products (musc, mov, softwar, txtbook. Amazon s onln product rvws rsmbl a J-shapd dstrbuton, whras th lab xprmntal data follow a unmodal, roughly normal dstrbuton. Furthrmor, whl th majorty of Amazon s onln product rvws ar xtrm or polarzd (on-star or fv-star, th majorty of th lab xprmnt s product rvws (ovr 90% ar modrat (two-star, thr-star, or four-star. Fnally, whl Amazon s onln product rvws ar mostly postv (fv-star, th lab xprmnt s rsults ar balancd across all star ratngs btwn on-star and fv-stars. Fgur B1. Comparson of Amazon s and th Lab Exprmnt s Dstrbutons of Onln Product Rvws MIS Quartrly Vol. 41 No. Appndcs/Jun 017 A7
Hu t al./slf-slcton Bass n Onln Product Rvws In addton to showng that th lab xprmnt s data follow a normal dstrbuton (Fgur B1, w solatd th two slf-slcton bass by plottng th dstrbuton of th rspondnts wth pror ownrshp (capturng acuston bas and rspondnts wth hgh ntntons ($3 to wrt an onln rvw on Amazon.com (capturng undrrportng bas. As shown n Fgur B for th mov DVDs (th othr products follow a smlar pattrn and ar omttd for brvty, pror ownrshp shfts th dstrbuton toward hghr ratngs. Bsds, slctng thos rspondnts wth hgh ntntons to wrt a rvw largly omts th modrat star ratngs, rsultng n a dstrbuton that rsmbls Amazon s obsrvd J- shapd dstrbuton. In sum, th combnaton of th two slf-slcton bass s shown to jontly shft a normal dstrbuton of all rspondnts to a lft-skwd bmodal dstrbuton, whch rsmbls Amazon s J-shapd dstrbuton. Fgur B. Dstrbuton of Onln Product Rvws from Amazon Vrsus Exprmntal Fld Study Rsults A8 MIS Quartrly Vol. 41 No. Appndcs/Jun 017
Hu t al./slf-slcton Bass n Onln Product Rvws Appndx C Comparson of Modls wth and Wthout Slf-Slcton Bass n Onln Product Rvws To compar th proposd dual mod modl aganst th thr comptng modls (man avrag modl, wghtd man avrag modl, and xtrm ratng controlld modl, w randomly slctd anothr 10,000 books, DVDs, and vdos from our Amazon sampl startng n July of 005, wth th SAS random functon. For ach product, w collctd ts prc, sals rank, and all onln product rvws for svral months on thr-day ntrvals. 9 Thrfor, snc w hav panl data from July 005 to January 006, w can compar whch modl has th hghst powr n trms of prdctng futur product sals usng longtudnal scondary data. Th modls, whos prdctv valdty s shown n Tabl C1, ar compard blow. Proposd Dual Mod Modl ln(salsrank + 1 = β 0 + β 1 AvgRatng t + β X Lt + β 3 X Ut + β 4 StdvRatng t + β 5 ln(salsrank t + β 6 ln(prc t + β 7 ln(numrv t + β 8 Book_Dummy + β 9 DVD_Dummy + ε t Modl 1 (Smpl Man ln(salsrank + 1 = α 01 + α 11 Man_Ratng + α 1 ln(sals_rank + α 31 ln(prc + α 41 ln(num_rv + α 51 Book_Dummy + α 61 DVD_Dummy + ε 1 Modl a (Wghtd Man a* ln(salsrank + 1 = α 0 + α 1 Wghtd_Man_Ratng 1 + α ln(salsrank + α 3 ln(prc + α 4 ln(num_rv + α 5 Book_Dummy + α 6 DVD_Dummy + ε Modl b (Wghtd Man b* ln(salsrank + 1 = α 03 + α 13 Wghtd_Man_Ratng + α 3 ln(salsrank + α 33 ln(amazon_prc + α 43 ln(num_rv + α 53 Book_Dummy + α 63 DVD_Dummy + ε 3 Modl c (Wghtd Man c* ln(salsrank + 1 = α 04 + α 14 Wghtd_Man_Ratng 3 + α 4 ln(salsrank + α 34 ln(prc + α 44 ln(num_rv + α 54 Book_Dummy + α 64 DVD_Dummy + ε 4 *Wghtd_Man_Ratng 1 = Avg((HlpfulRvws/TotalRvws * RvwRatng *Wghtd_Man_Ratng = Sum((HlpfulRvws/TotalRvws * RvwRatng/Sum(HlpfulRvws/TotalRvws *Wghtd_Man_Ratng 3 = Sum(HlpfulRvws * RvwRatng / Sum(HlpfulRvws 9 Idally, w would lk to collct data on a daly bass bcaus prc, sals, and onln product rvws chang on a daly bass. Howvr, du to th nstablty of Amazon s wb srvc, t oftn taks mor than thr days to collct a batch of data. Thus, to nsur that w gt clan copy for ach batch of data, w usd a thr-day nstad of a on-day ntrval. MIS Quartrly Vol. 41 No. Appndcs/Jun 017 A9
Hu t al./slf-slcton Bass n Onln Product Rvws Modl 3 (On-Star and Fv-Star Modl ln(salsrank + 1 = α 05 + α 15 Prcnt 1star + α 5 Prcnt 5star + α 35 ln(salsrank + α 45 ln(prc + α 55 ln(num_rv + α 65 Book_Dummy + α 75 DVD_Dummy + ε 5 As shown n Tabl C1, controllng for prvous sals rank, 10 prc, and th total numbr of product rvws, th modl wth slf-slcton controlld xplans a substantal amount of th varanc (R² adjustd = 77.9% n futur product sals, whch s sgnfcantly hghr than all othr modls (p <.0001. Th man of th onln product rvws has a sgnfcant ffct, xplanng.16% of th varanc n futur product sals. Th two dual mods X L and X U also hav sgnfcant ffcts (p <.001, 11 xplanng.64% and.33% of th varanc n futur product sals, rspctvly. Intrstngly, th varanc xpland by X L (lowr mod s almost twc as much as that xpland by th uppr mod X U. Ths fndngs ar consstnt wth th ltratur (.g., Chvalr and Mayzln 006 that suggsts that consumrs pay mor attnton to ngatv rvws (whch ar gnrally capturd by X L compard to postv rvws (whch ar capturd by X U. Fnally, th STD s statstcally sgnfcant (p<.05, xplanng.034% of th varanc. Ths s consstnt wth Clmons t al. (004 who showd that th varanc of onln product rvws affcts futur sals. Tabl C1. Modl Comparsons Proposd Modl X Modl 1 Modl a Modl b Modl c Modl 3 Man_Product Rvws -0.0513*** -0.0351*** -0.03** -0.07** -0.0194* X L 0.0573*** X U -0.0685*** STD 0.0086* Prcnt(1-star rvws 0.1088* Prcnt(5-star rvws -0.045 Ln (Currnt Sals Rank 0.7114*** 0.706*** 0.718*** 0.71*** 0.715*** 0.708*** ln(prc 0.0780*** 0.0999*** 0.100*** 0.0989** 0.0986*** 0.099*** ln (# of Product Rvws -0.0869*** -0.0533*** -0.056*** -0.050*** -0.051*** -0.058*** Book Dummy 0.311*** 0.334*** 0.333*** 0.331*** 0.390*** 0.333*** DVD Dummy -0.154*** -.104*** -0.105*** -0.108*** -0.108*** -0.105*** Intrcpt 3.7890*** 3.534*** 3.448*** 3.48*** 3.444*** 3.3936*** Adjustd R² 77.9% 75.18% 75.17% 75.5% 75.4% 75.17% Dffrnc n R².11%.1%.04%.05%.1% F-Valu 3.444*** 3.555***.666***.778*** 3.555*** N 7573 7573 7573 7573 7573 7573 STD s wghtd by hlpvot/totalvot. ***p <.001; **p <.01; *p <.05; +p <.10. All p-valus ar two-sdd. W usd th followng uaton for calculatng th sgnfcanc btwn two rgrsson modls: F ( kx k,( n kx k = [ ( _ ( _ ] 1 ( _ R Modl X R Modl K K [( R Modl X ] ( N Kx K x [7] 10 Th tm dffrnc btwn t + 1 and t s 130 days. W also tstd othr tm lag valus (.g., 100 days, 110 days, whch yldd smlar rsults. 11 Followng Agnr (1971, th varanc xpland was dcomposd among th ndpndnt varabls by multplyng th standardzd rgrsson coffcnts by th corrlaton of th ndpndnt varabls wth th dpndnt varabl. A10 MIS Quartrly Vol. 41 No. Appndcs/Jun 017
Hu t al./slf-slcton Bass n Onln Product Rvws whr K x s th numbr of ndpndnt varabls n th proposd Modl X K s th numbr of ndpndnt varabls n th comptng Modl I N s th sampl sz Thr ar svral crtra that can b usd to choos among comptng modls, such as th Adjustd R, Akak nformaton crtron (AIC, Schwarz nformaton crtron (SIC, Mallow s C p crtron, and forcast χ (ch-suar. Ths crtra am at mnmzng th rsdual sum of suars, or ncrasng th adjustd R valu. Th AIC mposs a harshr pnalty than th R, whl th SIC mposs an vn harshr pnalty than th AIC. Howvr, as argud by Dbold and Klan (001, no crtron s ncssarly supror. For smplcty, w valuatd th prformanc of th varous comptng modls by comparng thr adjustd R, whch s th most wdly usd crtron for modl comparson. In trms of othr comparsons byond th F-tst (Euaton 7, followng Davdson and MacKnnon (1993, p. 456: For lnar rgrsson modls, wth or wthout normal rrors, thr s of cours no nd to look at lklhood, W, and LR at all, snc no nformaton s gand from dong so ovr and abov what s alrady contand n F. Thrfor, w dd not prform othr comparsons for th nstd modls. For nonnstd modl comparson, w also usd th Davdson-MacKnnon J tst, whch showd smlar rsults. Th proposd slf-slcton controlld modl xplans at last % hghr varanc compard to th fv comptng modls (whch roughly xplan about th sam varanc. 1 Ths dffrnc n varanc xpland s statstcally sgnfcant (p <.0001, as th F-tsts n Tabl C1 attst. Bsds th hgh F-valus that dnot that th % mprovmnt n varanc xpland s statstcally sgnfcant, from a practcal standpont, on may uston ths mprovmnt. Howvr, t s mportant to rcognz that th grat majorty of th varanc s xpland by th control varabls. Spcfcally, th currnt sals rank xplans 5% of th varanc, 13 th numbr of onln product rvws xplans 4.55%, th product dumms xplan 7%, and prc only xplans.11%. Gvn ths nfluntal control varabls, th varanc xpland by th nw proposd ndpndnt varabls (X L, X U, STD s also substantal from a practcal standpont, attstng to th nd for ncludng ths dstrbutonal paramtrs whn prdctng futur product sals. Tabl C. Comparson btwn Proposd Mods and Prcntag of Polarzd Rvws Rgrsson Modl Man_Product Rvws -0.0906* X L 0.0563*** X U -0.0688*** STD 0.0083* % 1-star rvws -0.1895 N/S (p =.1739 % 5-star rvws 0.0343 N/S (p = 0.684 ln (Currnt Sals Rank 0.7115*** ln(prc 0.0778*** ln (# of Rvws -0.0866*** Book Dummy 0.318*** DVD Dummy -0.15*** Intrcpt 3.95*** Adjustd R² 77.9% N 7573 1 Intrstngly, non of th thr proposd wghtd mans of onln product rvws s supror to th smpl man ratng. Prhaps ths s bcaus consumrs only obsrv th smpl man and do not othrws procss th numbr of usful rvws. 13 W also ran th sam rgrsson modls (Tabl C1 by omttng th currnt sals rank as a control varabl, and th rsults wr vry smlar (Modl X outprformd all othrs by ovr %. Howvr, snc th varanc xpland n futur sals s substantally lowr (crca 35% whn omttng currnt sals rank, w only rport th rsults wth all control varabls. MIS Quartrly Vol. 41 No. Appndcs/Jun 017 A11
Hu t al./slf-slcton Bass n Onln Product Rvws Whl th proposd prdcton modl wth th proposd X L and X U mods s supror to th on wth th polarzd (on-star and fv-star rvws (Modl 3, w stll wantd to hav a drct comparson of thr jont mpact. Thrfor, w ran a rgrsson modl n whch w ncludd both X L and X U and also th prcntag of on-star and fv-star rvws (Tabl C. Th dnsty mass n th bmodal dstrbuton of onln product rvws that obtans th X L and X U ar dffrnt from th prcntag of on-star and fv-star rvws, allowng us to smultanously nclud thm n a rgrsson modl. As shown n Tabl C, both th prcntag of polarzd (1-star and 5-stars rvws bcom nsgnfcant whn X L and X U ar ncludd n th rgrsson modl. Accordngly, th ncluson of polarzd rvws dd not mprov th varanc xpland (77.9% n futur product sals. Ths rsults attst to th suprorty of th X L and X U paramtrs obtand by th DIP tst vrsus th prcntag of polarzd rvws. A1 MIS Quartrly Vol. 41 No. Appndcs/Jun 017
Hu t al./slf-slcton Bass n Onln Product Rvws Appndx D Proofs Proof of Lmma 1: Wth a wndow as dscrbd n Euaton [6], th dnsty functon of rvws s drvd as ( f 0 ( / φ ρ μ ρ ρ = δ + ( δ ( + ρ + Φ 1 Φ ρ ( f δ u E u δ Othrws [D1] Th xpctd ratng from consumr who purchass th product wth E(u $ 0 that s, $ α(p, wth α p, ( p + = ρ μ + ρ, s drvd by Er ( α = E ( α = f( d ρ ( μ φ δ+ + ρ ( μ ρ ρ = + ρ ( μ ( + d + δ + δ + Φ + (1 Φ ρ ρ + δ + + ρ ( μ = + ρ ( μ + ρ ρ ( μ φ ρ ρ d δ + δ + Φ + (1 Φ ρ ρ ( μ ρ ( μ φ δ + ρ ( μ ρ 1 ρ 1 ( 1 ρ ρ d δ + δ + Φ + (1 Φ ρ ρ ρ + ρ ( μ ρ ( μ φ ρ ( μ + ρ ρ δ + d δ + δ + ρ (1 1 ρ Φ + Φ ρ ρ = + ( + δ + δ + φ φ 1 ρ 1 ρ ρ μ 1 ρ Λ0 p whrλ0 = + ( + δ δ + Φ 1 Φ ρ ρ Q.E.D. [D] MIS Quartrly Vol. 41 No. Appndcs/Jun 017 A13
Hu t al./slf-slcton Bass n Onln Product Rvws Proof of Proposton 1: Followng [D], w drv th xpctd rvw scor from a consumr wth pror ualty xpctaton : ( = ( Er EE p ( ρ ( μ 1 ρ Λ 0 = E+ + p = + φ( α( p, + ρ 1 ρ p α p, Λ Φ 0 [D3] If w lt λ ( x φ = Φ ( ( x, thn [D3] can b xprssd as x ( 1 ρλ 0 ρλα (, Er = + + p p ρ λ α p, and ρ Λ0( ar th acuston bas and th undrrportng bas, rspctvly. If ρ 1, gttng rd of th undrrportng bas rurs Λ 0 = 0, whch can only b achvd whn δ and δ ar symmtrc n trms of th dffrnc btwn th ralzd ualty and pror, that s, δ + δ = (, f δ = δ = 0 s mpossbl du to th prvalnc of undrrportng bas. [D4] Th varanc of th ratng of consumr who purchass th product, E(μ $ p, s obtand by ( p + ρ μ Var( r α = Var( α = E( E( + ρ = E( ( 1 Λ ρ μ ρ 0 = E( ( (1 Λ = ρ μ ρ 0 δ + + ρ ( μ + δ + + ρ ( μ = (1 ρ (1 + Λ Λ Whr: ρ μ ρ μ φ ρ ρ d + δ + δ + Φ + (Φ 1 1 ρ ( ( ( ρ ρ μ ρ μ φ ρ ρ d (1 ρ Λ δ + δ + Φ + (1 Φ ρ ρ ( ( ( 1 0 0 [D5] Λ = 1 δ + δ + δ + δ + φ φ 1 ρ 1 ρ 1 ρ 1 ρ δ + δ + Φ + (1 Φ 1 ρ 1 ρ By th Law of Total Varanc and Euaton [D5] A14 MIS Quartrly Vol. 41 No. Appndcs/Jun 017
Hu t al./slf-slcton Bass n Onln Product Rvws Q.E.D. (( 1 E( Var( r1 = VarE r + r = Var( + ρ ( μ + 1 ρ Λ 0 + (1 ρ (1 +ΛΛ0 = ρ (1 λα ( λα α + (1 ρ (1 +Λ Λ 1 0 [D6] Proof of Corollary 1: Gvn p,, and Λ 0 ( = φ δ + δ + φ ρ 1 ρ δ + ( δ + ( + ρ Φ 1 Φ ρ 1 1 sgn E r Λ sgn 0 = δ + ( φ 1 ρ = sgn Φ = sgn φ δ + Φ ( δ + φ ρ ρ δ + 1 1 + δ + δ + Φ 1 Φ ρ ρ ρ δ + + δ + 1 Φ ρ ρ Φ δ + φ ρ ρ δ + 1 1 1 1 1 1 1 ( + ρ + 1 Φ δ ρ δ + = + δ + δ + δ + sgnφ Φ 1 Φ ρ ρ ρ + δ + δ + δ + φ φ φ ρ ρ ρ = + + + + δ δ δ δ + sgn φ Φ 1 Φ ρ 1 ρ 1 ρ 1 ρ + + + δ δ δ + φ φ φ ρ ρ ρ 1 E( r δ + δ + Thus th sgn of dpnds on th comparson of th and. Whn < Λ that s, ρ ρ 0, δ + < Λ 0 1 ρ, th last xprsson s postv, Λ 0 1 > 0. That s, th xpctd ratng ncrass wth δ and vc vrsa. E r MIS Quartrly Vol. 41 No. Appndcs/Jun 017 A15
Hu t al./slf-slcton Bass n Onln Product Rvws Λ 0 (. E( r Smlar to th abov rsults, th sgn of dpnds on th sgn of sgn E r sgn = Λ 0 δ + φ = + [ 1 ρ δ + δ + δ + sgn Φ 1 Φ φ ρ ρ ρ δ + δ + ΦΦ ρ + δ + 1 Φ φ ρ ρ 1 + ( + ( + ( = ( + δ δ δ sgn φ Φ 1 Φ 1 ρ 1 ρ 1 ρ + ( δ φ ρ δ + δ + Φ φ ρ ρ = + δ + δ + δ + δ + sgn Φ 1 Φ ρ ρ ρ φ 1 1 1 ρ δ φ + ρ 1 Λ δ + Whn <, that s, th xpctd ratng dcrass wth δ, and vc vrsa. ρ 0 δ + E( r < Λ 0 1 ρ, < 0, Q.E.D. Proof to Corollary : ( Λ 0 ( By Proposton 1, th xpctd consumr ratng n a sngl prod s p + ρ λ α, + ρ p and varanc ( 1 ( ( ( ( 1 ( 1 1 0 p p p + + Λ Λ ρ λα, λα, α, ρ. Snc consumrs n dffrnt prods ar updatng thr ualty blfs basd on Euaton [10], = ω + ω E r. If consumrs can fully ovrcom both typs of bass, thn ( ( 1. = t + t + 1 Plug nto Proposton 1, thn th man of th ratng srs kps th sam ovr tm: + ρ λ α p, + ρ Λ p and varanc also dos not chang ovr tm ( p ( ( p ( p + ( ( 1 + ΛΛ0 ρ λα λα α ρ,,,. Thus th ratng srs s statonary. ( If consumrs form ualty xpctaton wthout th bass n th prvous prods, and ρ λ( α Er = + p, + ρ p, t Λ 0 ( 1 ( ( ( 1 ( 1 Λ1 Λ0 Var r = ρ λα p, λα, α p, + ρ +. t tm prods corr(r t, r t+1 thus ratng srs ar ndpndnt. Q.E.D. t = t= 1 Th corrlaton btwn ratngs n dffrnt A16 MIS Quartrly Vol. 41 No. Appndcs/Jun 017
Hu t al./slf-slcton Bass n Onln Product Rvws Rfrncs Agnr, D. J. 1971. Basc Economtrcs, Uppr Saddl Rvr, NJ: Prntc Hall Andrson, E. W. 1998. Customr Satsfacton and Word of Mouth, Journal of Srvc Rsarch (1:1, pp. 5-17. Andrson, T. W. 005. Orgns of th Lmtd Informaton Maxmum Lklhood and Two-Stag Last Suars Estmators, Journal of Economtrcs (17, pp. 1-16. Chakravart, I. M., Laha, R. G., and Roy, J. 1967. Handbook of Mthods of Appld Statstcs, Nw York: John Wly and Sons. Chn, P-Y., Wu, S-Y., and Yoon, J. 004. Th Impact of Onln Rcommndatons and Consumr Fdback on Sals, n Procdngs of th 5 th Intrnatonal Confrnc on Informaton Systms, Washngton, D.C., pp. 711-74. Chng, M-Y., and Hall, P. 1998. Calbratng th Excss Mass and Dp Tsts of Modalty, Journal of th Royal Statstcal Socty B (60:3, pp. 579-589 Chvalr, J., and Mayzln, D. 006. Th Effct of Word of Mouth on Sals: Onln Book Rvws, Journal of Marktng Rsarch (43:3, pp. 345-354. Chntagunta, P., Erdm, T., Ross, P. E., and Wdl, M. 006. Structural Modlng n Marktng: Rvw and Assssmnt, Marktng Scnc (5:6, pp. 604-616. Clmons, E. K., Gao, G., and Htt, L. M. 006. Whn Onln Rvws Mt Hypr Dffrntaton: A Study of th Craft Br Industry, Journal of Managmnt Informaton Systms (3:, pp. 149-171. Davdson, R., and MacKnnon, J. G. 1993. Estmaton and Infrnc n Economtrcs, Oxford, UK: Oxford Unvrsty Prss. Dbold, F., and Klan, L. 001. Masurng Prdctablty: Thory and Macroconomc Applcatons, Journal of Appld Economtrcs (16:6, pp. 657-669. Hartgan, J. A., and Hartgan, P. M. 1985. Th DIP Tst of Unmodalty, Annals of Statstcs (13:1, pp. 70-84. Hndrson, R., Dggl, P. J., and Dobson, A. 000. Jont Modlng of Longtudnal Masurmnts and Evnt Tm Data, Bostatstcs (1, pp. 465-480. Mullr, D. W., and Sawtzk, G. 1991. Excss Mass Estmats and Tsts of Multmodalty, Journal of th Amrcan Statstcal Assocaton (86, pp. 738-746. Slvrman, B. W. 1981. Usng Krnl Dnsty Estmats to Invstgat Multmodalty, Journal of th Royal Statstcal Socty (43:1, pp. 97-99. Stphns, M. A. 1974. EDF Statstcs for Goodnss of Ft and Som Comparsons, Journal of th Amrcan Statstcal Assocaton (69, pp. 730-737. Thod Jr., H. C. 00. Tstng for Normalty, Nw York: Marcl Dkkr. MIS Quartrly Vol. 41 No. Appndcs/Jun 017 A17