Table 1 Description of the traffic light system based on psychometric proprieties (A = Green, B = Amber and C = Red)

Acceptability

A: The percentage of missing data: ≤ 5%

B: The percentage of missing data: >  5% ≤ 40%

C: The percentage of missing data: > 40%

Targeting

A: End-point categories ≤5%

B: End-point categories > 5% ≤ 40%

C: End-point categories > 40%

Internal consistency reliability

A: 0.95 ≥ Cronbach’s α ≥ 0.70

B: 0.70 > Cronbach’s α ≥ 0.60 or Cronbach’s α > 0.95

C: Cronbach’s α ≥ 0.60

Item dependency

A: Inter-item correlations < 0.3

B: Inter-item correlations ≥0.3 < 0.6

C: Inter-item correlations ≥0.6

Response categories

A: All the categories are ordered and evenly spaced

B: All the categories are ordered but categories are nor evenly spaced

C: Disordered categories

Item fit statistics

A: Item with infit and outfit mean square (MNSQ): 0.70–1.30

B: Item fit statistics outside 0.70–1.30 limit but within 0.5–1.5 limit

C: Item fit statistics outside 0.5–1.5 limit

Differential Item Functioning (DIF) (assessed for gender and service type)

DIF tests whether population subgroups respond to an item differently. It is assessed by examining the mean difference in item measure between the groups. DIF was assessed for gender (male vs female), age groups (65–74 yrs vs 75–84 yrs vs 85 yrs+) and service (Commonwealth Home Support Program vs Home Care Packages).

A: DIF ≤ 0.5 logits

B: DIF > 0.5 ≤ 1.00 logits

C: DIF > 1.0 logits

Item Information Function (IIF)

IFF is the amend of information an item possesses. It is observed in a graph which is plotted between item information level (range from 0 to 1) on the Y-axis and relative item measure in logits on the X-axis.

A: Item with high-level information and wider measurement range (a bell-shaped graph)

B: Item with low-level information and wider measurement range/item with high information and narrow measurement range

C: Item with a low-level information and narrow measurement range