Association of longitudinal pet ownership with wheezing in 3-year-old children using the distributed lag model: the Japan Environment and Children’s Study

Table 2 Simulation experiment results: empirical squared error

time	γ=0			γ=0.975			γ=0.9999
time	Single	Multi	DLM	Single	Multi	DLM	Single	Multi	DLM
Scenario 1
6	6.9	7.0	6.4	6.1	12.5	8.2	6.1	51.7	18.2
12	7.1	7.2	4.4	6.1	15.2	4.4	6.0	61.3	12.1
18	7.0	7.1	4.2	6.1	15.4	4.3	6.1	62.3	9.2
24	7.4	7.4	3.6	6.0	14.9	3.5	6.1	61.5	7.8
30	7.2	7.3	3.4	6.0	14.8	3.4	6.1	60.0	8.4
36	7.4	7.3	3.7	6.1	14.9	3.9	6.1	63.6	9.2
42	7.4	7.4	3.8	6.0	15.3	4.0	6.1	63.4	9.1
48	7.1	7.1	3.5	6.0	15.1	3.1	6.1	59.4	8.4
54	7.2	7.2	3.6	6.2	15.6	3.2	6.1	62.7	10.2
60	6.9	7.0	5.7	6.0	12.4	7.1	6.1	51.9	17.5
Scenario 2
6	7.2	7.2	6.7	6.5	12.8	8.5	6.1	51.3	17.4
12	7.2	7.3	4.4	6.3	14.6	4.3	6.1	61.8	12.0
18	7.2	7.2	4.2	6.3	14.9	4.4	6.1	61.0	9.2
24	7.0	7.0	3.6	6.3	15.7	3.6	6.1	62.4	7.7
30	7.2	7.2	3.4	6.4	15.2	3.4	6.1	61.7	8.4
36	7.2	7.2	3.7	6.3	15.3	3.8	6.1	64.9	9.4
42	7.1	7.1	3.8	6.3	15.2	3.8	6.1	61.6	9.3
48	6.8	6.8	3.5	6.3	15.0	3.1	6.1	63.2	8.3
54	7.5	7.6	3.9	6.3	15.2	3.3	6.0	62.5	9.8
60	7.4	7.4	6.3	6.4	12.6	7.2	6.0	50.8	17.4
Scenario 3
6	8.2	8.2	7.6	7.3	14.6	9.8	7.5	56.9	21.4
12	8.0	8.0	5.1	7.3	16.9	5.1	7.5	67.9	14.5
18	8.1	8.1	4.8	7.4	17.2	5.2	7.5	67.1	11.1
24	7.8	7.8	4.0	7.4	17.4	4.2	7.4	69.4	9.7
30	7.9	7.9	3.7	7.5	17.6	4.0	7.5	68.9	10.6
36	7.6	7.6	4.0	7.3	17.4	4.6	7.5	68.3	11.6
42	7.8	7.8	4.1	7.1	17.5	4.6	7.5	67.9	11.3
48	7.9	8.0	3.9	7.2	17.6	3.6	7.4	67.7	10.0
54	8.0	8.1	4.2	7.3	16.9	3.7	7.4	67.5	12.4
60	8.2	8.2	6.7	7.2	14.4	8.5	7.4	56.5	22.2

Empirical standard errors rounded to the fourth place and multiplied by \({10}^{2}\)
Single, the exposure at each time point is used in a separate regression model; Multi, the exposures at each time point are simultaneously entered into a single regression model; DLM, the Distributed Lag Model
γ represents the correlation used to generate data between exposures.
Scenario 1: Exposure effects are constant regardless of time point. Scenario 2: Exposure effects’ magnitude is an upward convex quadratic curve. Scenario 3: Exposure effects exist only from \(t = 36 \text{ to } 47\)

ISSN: 1476-069X