Table 1 Model fit statistics and type 3 tests of fixed effects for nine mixed effects logistic regression models estimating the probability of smoking menthol cigarettes among US adults who currently smoke from 2002 to 2020

Statistic

# of Model Parameters

29

40

30

30

30

31

31

32

32

Log L

23555.83

23529.13

23553.18

23553.60

23555.33

23546.93

23545.16

23486.97

24520.09

AIC

23613.83

23609.13

23613.18

23613.60

23615.33

23608.93

23607.16

23550.97

24584.09

BIC

23619.55

23617.01

23619.10

23619.52

23621.24

23615.04

23613.27

23557.28

24520.09

Fixed effects: Type 3 F test (p-value)

Female

6.54 (0.011)

6.62 (0.010)

6.65 (0.010)

6.68 (0.010)

6.52 (0.011)

6.54 (0.011)

6.59 (0.010)

6.68 (0.010)

40.48 (< 0.001)

Age group

52.69 (< 0.001)

44.99 (< 0.001)

46.72 (< 0.001)

46.68 (< 0.001)

51.06 (< 0.001)

48.00 (< 0.001)

47.58 (< 0.001)

46.42 (< 0.001)

44.78 (< 0.001)

Race/ethnicity

181.24 (< 0.001)

172.30 (< 0.001)

180.74 (< 0.001)

179.81 (< 0.001)

179.57 (< 0.001)

179.26 (< 0.001)

178.73 (< 0.001)

75.42 (< 0.001)

506.12 (< 0.001)

SES

1.34 (0.261)

1.25 (0.287)

1.33 (0.263)

1.34 (0.263)

1.34 (0.261)

1.35 (0.260)

1.35 (0.258)

1.37 (0.255)

10.09 (< 0.001)

lfParticC

6.63 (0.010)

3.40 (0.065)

6.37 (0.012)

7.44 (0.006)

10.57 (0.001)

2.97 (0.085)

3.88 (0.049)

3.69 (0.055)

0.08 (0.772)

Female X race/ethnicity

1.16 (0.324)

1.18 (0.316)

1.19 (0.312)

1.19 (0.314)

1.16 (0.324)

1.19 (0.311)

1.19 (0.313)

1.13 (0.335)

1.69 (0.166)

Age group X race/ethnicity

13.48 (< 0.001)

14.09 (< 0.001)

13.57 (< 0.001)

13.54 (< 0.001)

13.73 (< 0.001)

14.00 (< 0.001)

13.91 (< 0.001)

11.96 (< 0.001)

12.38 (< 0.001)

Female X age group

2.49 (0.083)

3.15 (0.043)

2.59 (0.075)

2.61 (0.073)

2.49 (0.083)

2.52 (0.080)

2.56 (0.077)

0.84 (0.433)

0.36 (0.697)

Female X age group X race/ethnicity

2.35 (0.028)

2.14 (0.045)

2.30 (0.032)

2.32 (0.031)

2.37 (0.028)

2.20 (0.040)

2.22 (0.038)

2.12 (0.048)

1.04 (0.394)

Temporal Effects

time (dummied)

19132.8 (< 0.001)

time (linear/PWLT)

9.14 (0.003)

0.31 (0.577)

0.67 (0.412)

3.96 (0.047)

0.05 (0.826)

0.21 (0.643)

0.16 (0.688)

4.33 (0.037)

timeCC (PWLT)

0.69 (0.407)

7.61 (0.006)

lagCC (PWLT)

0.57 (0.452)

14.82 (< 0.001)

15.94 (< 0.001)

14.06 (< 0.001)

time4CV (PWLT)

0.10 (0.751)

3.30 (0.069)

5.98 (0.015)

6.11 (0.013)

27.91 (< 0.001)

Random effects (std err)

Census division: intercept

0.0895 (0.0319)

0.0898 (0.0325)

0.0896 (0.0319)

0.0895 (0.0318)

0.0894 (0.0317)

0.0892 (0.0317)

0.0890 (0.0316)

0.1569 (0.0573)

0.0664 (0.0321)

Race/ethnicity: intercept\( {}^{\text{*}}\)

0.1015 (0.0393)

Survey wave: intercept

0.0005 (0.0013)