SUPPLEMENTARY MATERIALS RASCH ANALYSIS Rsch nlyses were used to estimte item nd person mesures for three sets of questions, detiled below (Tble S1), nd to exmine response ctegory functioning, person nd item seprtion sttistics, infit nd outfit men-squre (MnSq) sttistics, nd item trgeting for ech set of questions. All Rsch nlyses were performed with Winsteps softwre version 3.90 1 ccording to the Andrich rting scle model for polytomous dt using joint likelihood estimtion. 2 There were no significnt differentil item functioning (DIF) effects cross groups. 1
Tble S1: Summry of items in ech of the three sets of questions nlyzed with Rsch Anlysis Visul difficulty without bioptic Bioptic helpfulness Items Reding rod/trffic signs; Reding street nme signs; Identifying trffic light signls; Seeing brke lights/turn signls on vehicles hed; Judging the distnce to crs in front; Looking for pedestrins / other hzrds on rod hed; Judging when sfe to pss nother cr on 2-lne rod; Judging when sfe to move t n intersection without trffic lights; Judging when sfe to merge on freewy; *Checking the speedometer. Sme items s visul difficulty scle Scoring Rting of the degree of perceived (visul) difficulty without bioptic telescope for ech item: 1 = Extreme difficulty 2 = Moderte difficulty 3 = Some difficulty 4 = A little difficulty 5 = No difficulty N/A = not pplicble # Rting of bioptic helpfulness for ech item (tsk) for which bioptic ws used 0 = Bioptic telescope not used 1 = Does not help t ll 2 = A little helpful 3 = Somewht helpful 4 = Modertely helpful 5 = Very helpful N/A = not pplicble # Driving difficulty In rin Alone Prllel prking Left turn Highwys (intersttes, expresswys) High-trffic rods Rush hour At night In bright sunshine Rting of driving difficulty for ech item (sitution) 0 = Not driven in this sitution for resons other thn vision 1 = Avoid driving becuse of vision, 2 = Extreme difficulty 3 = Moderte difficulty 4 = A little difficulty 5 = No difficulty * Item excluded from nlyses becuse this is not tsk for which bioptic telescope is normlly used. # Not pplicble responses were treted s missing dt 2
Perceived visul difficulty without the bioptic In the initil Rsch nlysis, we found the Andrich thresholds did not dvnce monotoniclly (referred to s disordering of step clibrtion). A filure of the Andrich thresholds to dvnce implies n irregulr pttern of response ctegory usges. 3 To ddress this, we collpsed djcent ctegories Some difficulty nd ctegory A little difficulty (Figure S1). An exmintion of person misfits scores led to the exclusion of two individuls becuse their responses were the opposite of wht ws expected by the model (i.e., reported no difficulty when reding rod/trffic signs nd extreme difficulty when judging distnces between crs). Results from the Rsch nlysis of the remining persons re presented for dt pooled cross the three groups in Tble S2 nd for ech group seprtely in Tble S2b. After collpsing the responses into the four ctegories, the seprtion nd relibility indices were cceptble for both person mesures nd item mesures. The men item mesure is lwys plced t 0, so looking t the men person mesure revels how well the items mtch the bility of the popultion. As cn be seen in Tble S2, the person mesure of 7 logits indictes tht the men difficulty of the items ws resonbly well mtched to the men bility of the persons. 3
Ctegory probbility curves with disordered step clibrtions Ctegory probbility curves fter collpsing djcent ctegories -6-4 -2 0 2 4 6-6 -4-2 0 2 4 6 Extreme difficulty Some difficulty No difficulty Moderte difficulty A little difficulty Extreme difficulty Some/Little difficulty Moderte difficulty No difficulty Figure S1: Ctegory probbility curves for visul difficulty without bioptic: () The originl five response ctegories; nd (b) After collpsing djcent ctegories some nd little difficulty to crete four response ctegories to ddress the irregulr pttern of response ctegory usge seen in () Tble S2. Finl prmeters for person nd item mesures (pooled cross groups) from the Rsch nlysis of the items bout the perceived visul difficulty during specific driving tsks without bioptic telescope n Mesure (logits) b Seprtion c Relibility d Infit MnSq e Outfit MnSq e Person 113 7 ± 1.40 2.02 0 8 ± 8 6 ± 8 Item 9 0 ± 1.74 11 9 3 ± 4 6 ± 7 Note. Men ± SD One person removed due to extreme responses contrdictory to model expecttions nd two persons removed due to lck of responses. b Men person bility mesure ner 0 indictes good trgeting of questionnire; Men item difficulty is lwys set to 0. c Seprtion indices indicte how well the questionnire differentites between persons nd items; the greter the index, the better the seprtion. d Person nd item seprtion relibility vlues re cceptble. 4 e The model expecttion for item infit nd outfit men squre is 1. 4
Tble S2b. Finl prmeters for person mesures for ech group from the Rsch nlysis of the items bout the perceived visul difficulty during specific driving tsks without bioptic telescope n Mesure (logits) b Seprtion c Relibility d Infit MnSq e Outfit MnSq e Non-AMD FlwB 47 5 (4) 1.51 9 4 ± 1 7 ± 3 Non-AMD FLwoB 38 2 (1) 2.07 1 2 ± 7 2 ± 9 AMD 28-9 (8) 2.72 8 1.13 ± 9 9 ± 7 Note. AMD: Age-relted mculr degenertion; FLwB: first licensed with bioptic; FLwoB: first licensed without bioptic One person removed due to extreme responses contrdictory to model expecttions nd two persons removed due to lck of responses. b Men person bility mesure ner 0 indictes good trgeting of questionnire. Lrger vlue indictes less perceived visul difficulty. Men (SE). c Seprtion indices indicte how well the questionnire differentites between persons; the greter the index, the better the seprtion. d Person seprtion relibility vlues re cceptble. 4 e The model expecttion for item infit nd outfit men squre is 1. Men ± SD. Perceived helpfulness of bioptic telescope In the initil Rsch nlysis, we found the Andrich thresholds did not dvnce monotoniclly (disordering of step clibrtion), nd the verge ctegory mesures did not dvnce monotoniclly (disordering of the ctegory mesure). A filure of the Andrich thresholds to dvnce implies n irregulr pttern of response ctegory usges, wheres disordering of the ctegory mesures indictes some systemtic difference contrdicting the Rsch model ssumption tht higher mesures men higher scores on the rting scle. 3 In ddition, ctegory Does not help hd only three observtions which is considered too smll for stble estimtion of the Andrich threshold. 3 To ddress these problems, we collpsed ctegory Do not use nd ctegory Does not help, nd collpsed together ctegory A little helpful, ctegory Somewht helpful, nd ctegory Modertely helpful ; thus there were only three ctegories in the finl nlysis (Figure S2). Results from the Rsch nlysis for dt pooled cross the three groups re presented in Tble S3 nd for ech group seprtely in Tble S3b. As cn be seen in Tble S3, fter collpsing the responses into three ctegories, the item seprtion nd relibility were good. The men person mesure of 3 logits indictes tht the men difficulty of the items ws well mtched to the men bility of the persons. However, the person seprtion nd relibility did not meet the minimum cceptble vlues (2.00 nd 0, respectively), lthough they were close to the minimum. This suggests tht the items were not 5
very good t distinguishing different levels of person s perceived helpfulness. This is most likely due to so few people reporting the bioptic telescope s less thn somewht helpful in every driving tsk. Ctegory probbility curves with disordered step clibrtions nd disordered ctegory mesures Ctegory probbility curves fter collpsing djcent ctegories -5-4 -3-2 -1 0 1 2 3 4 5-5 -4-3 -2-1 0 1 2 3 4 5 Do not use A little helpful Modertely helpful Does not help Somewht helpful Very helpful Do not use/does not help Somewht/A little/modertely helpful Very helpful Figure S2: Ctegory probbility curves for bioptic helpfulness questions: () The originl six response ctegories; nd (b) After collpsing djcent ctegories to crete three response ctegories to ddress the problems of infrequent nd irregulr ptterns of response ctegory usge seen in () Tble S3. Finl prmeters for person nd item mesures (pooled cross groups) from the Rsch nlysis of the items on perceived helpfulness of the bioptic telescope during specific driving tsks. n Mesure (logits) b Seprtion c Relibility d Infit MnSq e Outfit MnSq e Person 115 3 ± 1.46 1.71 5 7 ± 4 0 ± 8 Item 9 0 ± 1.56 8.10 8 1 ± 6 0 ± 1 Note. Men ± SD One subject with insufficient dt excluded b Men person bility mesure ner 0 indictes good trgeting of questionnire; Men item difficulty is lwys set to 0. c Seprtion indices indicte how well the questionnire differentites between persons nd items; the greter the index, the better the seprtion. d Person nd item seprtion relibility vlues re cceptble. 4 e The model expecttion for item infit nd outfit men squre is 1. 6
Tble S3b. Finl prmeters from the Rsch nlysis of the items on perceived helpfulness of the bioptic telescope during specific driving tsks by group. n Mesure (logits) b Seprtion c Relibility d Infit MnSq e Outfit MnSq e Non-AMD FlwB 47 2 (7) 1.45 8 0 ± 1 7 ± 4 Non-AMD FLwoB 38-1 (4) 1.93 9 0 ± 4 3 ± 1 AMD 30 6 (4) 2.12 2 1.21 ± 7 1.27 ± 1.19 Note. AMD: Age-relted mculr degenertion; FLwB: first licensed with bioptic; FLwoB: first licensed without bioptic One subject with insufficient dt excluded b Men person bility mesure ner 0 indictes good trgeting of questionnire. Lrger vlue indictes less perceived helpfulness. Men (SE). c Seprtion indices indicte how well the questionnire differentites between persons; the greter the index, the better the seprtion. d Person seprtion relibility vlues re cceptble. 4 e The model expecttion for item infit nd outfit men squre is 1. Men ± SD. Perceived difficulty with driving As in the other Rsch nlyses, we found disordering of the Andrich thresholds. In ddition, ctegory Extreme difficulty hd only nine responses which is considered too low for stble estimtion of the Andrich threshold. 3 To ddress this, we collpsed ctegory Don t due to vision nd ctegory Extreme difficulty (Figure S3). Results from the Rsch nlysis for dt pooled cross the three groups re presented in Tble S4 nd for ech group seprtely in Tble S4b. As with the items on perceived helpfulness of the bioptic telescope, the item seprtion nd relibility were cceptble for perceived visul difficulty in specific driving situtions, but the person seprtion nd relibility were not (Tble S4). The men person mesure (1.88 logits) indictes tht the person s perceived bility fr exceeded the difficulty level required by the items. This is lso observed in the item-person mp where t lest hlf the smple flls bove the items rted s the most difficult (Figure 5 in min mnuscript). This mismtch between the perceived bilities nd the item difficulty contributes to the uncceptble vlues for the person mesure seprtion nd relibility indices. The person seprtion nd relibility could be improved by creting more questions better tilored for the bilities of the popultion. 7
Ctegory probbility curves with disordered step clibrtions Ctegory probbility curves fter collpsing djcent ctegories -5-4 -3-2 -1 0 1 2 3 4 5-5 -4-3 -2-1 0 1 2 3 4 5 Don't due to vision Moderte difficulty No difficulty Extreme difficulty A little difficulty Don't due to vision/extreme difficulty Moderte difficulty A little difficulty No difficulty Figure S3: Ctegory probbility curves for perceived difficulty with driving: () The originl five response ctegories; nd (b) After collpsing djcent ctegories to crete four response ctegories to ddress the problems of infrequent nd irregulr ptterns of response ctegory usge seen in () Tble S4. Finl prmeters for person nd item mesures (pooled cross groups) from the Rsch nlysis of the items bout the perceived visul difficulty during specific driving situtions. n Mesure (logits) b Seprtion c Relibility d Infit MnSq e Outfit MnSq e Person 115 1.88 ± 1.33 7 3 8 ± 8 1 ± 8 Item 9 0 ± 8 3.62 3 1.10 ± 2 0 ± 6 Note. Men ± SD One subject with insufficient dt excluded b Men person bility mesure ner 0 indictes good trgeting of questionnire; Men item difficulty is lwys set to 0. c Seprtion indices indicte how well the questionnire differentites between persons nd items; the greter the index, the better the seprtion. d Person nd item seprtion relibility vlues re cceptble. 4 e The model expecttion for item infit nd outfit men squre is 1. 8
Tble S4b. Finl prmeters from the Rsch nlysis of the items bout the perceived visul difficulty during specific driving situtions by group. n Mesure (logits) b Seprtion c Relibility d Infit MnSq e Outfit MnSq e Non-AMD FlwB 47 1.95 (7) 9 4 8 ± 2 6 ± 6 Non-AMD FLwoB 38 1.94 (4) 1.19 9 3 ± 1 3 ± 7 AMD 30 1.69 (6) 1.32 4 1.15 ± 3 1 ± 5 Note. AMD: Age-relted mculr degenertion; FLwB: first licensed with bioptic; FLwoB: first licensed without bioptic One subject with insufficient dt excluded b Men person bility mesure ner 0 indictes good trgeting of questionnire. Lrger vlue indictes less perceived visul difficulty. Men (SE). c Seprtion indices indicte how well the questionnire differentites between persons; the greter the index, the better the seprtion. d Person seprtion relibility vlues re cceptble. 4 e The model expecttion for item infit nd outfit men squre is 1. Men ± SD. References 1. Lincre JM. Winsteps Rsch Mesurement Softwre. Chicgo: winsteps.com; 2015. 2. Bond T, Fox CM. Applying the Rsch Model: Fundmentl Mesurement in the Humn Sciences. 3rd ed. New Jersey: Lwrence Erlbum Assocites; 2015. 3. Lincre JM. Optimizing rting scle ctegory effectiveness. J Appl Mes. 2002;3:85-106. 4. Pesudovs K, Burr JM, Hrley C, Elliott DB. The development, ssessment, nd selection of questionnires. Optom Vis Sci. 2007;84:663-674. 9