Participants

We recruited our sample of college students from three schools of higher education in Canton de Vaud in Switzerland (the Swiss Federal Institute of Technology in Lausanne (EPFL), the University of Lausanne (UNIL) and Ecole hoteliere de Lausanne (EHL)). College students from these three schools can register to the Laboratory of Behavioral Experiments program at the University of Lausanne and participate in experiments and surveys. The online questionnaire we used was created on Qualtrics and sent out to all students who registered in the University of Lausanne’s experiment program. The invitation email we sent to students and the introductory page of our online survey did not mention the specific aim of the study but referred to it as a study on their quality of life in general. 6,578 emails were sent, out of which 1,938 students completed our survey in the following two weeks (response rate = 29.5%). For their participation, students who completed our online survey were automatically entered into a lottery for which the highest prize was about USD 300. The experimental protocol and informed consent were approved by HEC Ethics Committee of the University of Lausanne in February 2017, and all subjects gave informed consent.

Out of the 1,938 college students who completed our online questionnaire, we kept those who were between 18 and 25 years old to capture “standard” college progression. This age restriction also corresponds to late adolescent/young adulthood [69], which represents a period in life with important transitions from adolescence to adulthood [70] that coincide with major changes both in mental health and sleep patterns/circadian rhythm [10–15]. Out of 1,938 students who answered our survey, only 3 respondents were 17 years old (as compared to 160 college students who were 18 years old), while 78 respondents were 25 years old, as opposed to 39 respondents who were 26. After discarding 125 observations that were out of the age range, our final sample consisted of 1,813 observations.

Survey design and measurements

After completing the consent forms, college students were first asked to evaluate our set of five sleep-related anchoring vignettes using a VAS ranging from 0 (‘no difficulty’) to 100 (‘extreme difficulty’). We then asked them to evaluate their own sleep difficulties, using the same VAS. As discussed in Hopkins and King (2010) [61], asking individuals to evaluate anchoring vignette first allows to prime respondents into interpreting the self-assessment question in a similar light and defining the response scale in a common way. The self-assessment question was then followed by a series of more general questions on socio-demographic characteristics from which we derive information to create our set of control variables.

Statistical methods

To gain a preliminary understanding of the existence and strength of the correlation between sleep difficulties and depressive symptoms in our college student population, we first use Epanechnikov kernel densities to investigate the bivariate relationship between these two variables. We further investigate the relationship between sleep difficulties and depressive symptoms using multivariate linear regressions, including various socio-demographic characteristics and self-reported measures of sleep patterns that are not subject to reporting heterogeneity, e.g., hours of sleep, as control variables. The use of linear specifications is supported by various tests we implement and report in S5 Appendix.

We then explore two different ways to determine the existence and influence, if any, of reporting heterogeneity in subjective sleep difficulties. Perhaps the first and most straightforward way to control for reporting heterogeneity in our setting is to include vignette evaluations as additional controls in the linear regressions. This assumes that respondents use the same reporting scale when evaluating their own sleep difficulties as the scale they use when evaluating the sleep difficulties of the person described in the anchoring vignettes. This strategy, however, does not allow us to determine what the characteristics of the individuals that drive reporting heterogeneity are. Another way to disentangle reporting heterogeneity and sleep difficulties is to perform a double-index model [60]. This model exploits respondents’ evaluations of sleep difficulties for themselves and for vignettes, assuming that individuals use the same reporting scales. Under this assumption, one can control for reporting heterogeneity as one controls for individual fixed effects in panel data models (where several observations are recorded for the same individual over time). The advantage is that the model allows us to not only control for reporting heterogeneity but also estimate the characteristics of the individuals that drive reporting heterogeneity.

More formally, we assume $$ y_{i0}^{*}$$, the latent level of sleep difficulties of respondent i, can be modeled as a linear function of a set of factors $$ x_i^{\prime }$$ subject to an error term ϵ_i0:

When the level of sleep difficulties $$ y_{i0}^{*}$$ is self-reported, the measurement can be potentially biased due to reporting heterogeneity, i.e., respondents with different characteristics report value of $$ y_{i0}^{*}$$ in systematically different ways. By assuming that reporting heterogeneity can take the form of an additive and unobserved individual effect c_i, the reported value of sleep difficulties of respondent i, y_i0, takes the form:

In addition to these assumptions, the use of anchoring vignettes to correct for reporting heterogeneity requires the very common vignette-related assumptions, namely, vignette equivalence and response consistency [45, 47, 55, 62, 63]. Vignette equivalence assumes that vignettes are perceived in the same way by all respondents up to an idiosyncratic error term. Under this assumption, the perception of vignette j is:

By defining c_i as a linear function of x_i, i.e., $$ c_i=x_i^{\prime }\gamma $$, we can plug in $$ y_{i0}^{*}$$ into Eq 2 and $$ y_{ij}^{*}$$ into Eq 4 to obtain the following system of equations:

We can then simultaneously estimate this system of equations with OLS, where b₀ represents the “true” effect of x on subjective sleep difficulties and γ represents the effects of x on reporting heterogeneity c.

Descriptive statistics

Table 1 reports the descriptive statistics of our study sample. The average score of sleep difficulty is 37.7, on a scale where 0 represents “no difficulty” and 100 “extreme difficulty”. Up to 16%, 6% and 1.8% of the college students in our sample have mild, moderate, or severe depressive symptoms, respectively, as reflected by their PHQ-9 score. Females account for 51% of our sample. More than half (52%) of our respondents are Swiss, and a significant portion of them are coming from Western Europe (35%) and Africa (7.3%). Most of the respondents are undergrad students (82%). 34% of our respondents are from families that are making between USD 7,000 and 12,000 per month, which is comparable to the average gross income per month per household in Switzerland in 2014 (about USD 10,0798). 51% of our respondents claim they are single at the time of the online survey, 2.4% admit to have no close friends and 7.7% have no siblings. Among our respondents, about 3% of them evaluate the relationship with their parents as being bad. More than half of them consider their school performance as average and another 13% think their performance to be below average.

Table 1

Descriptive statistics (N = 1, 813).

Variable	Mean	SD	Min	Max
Sleep difficulty (VAS score)	37.7	27.4	0	100
Depressive symptoms (based on PHQ-9 score)
No or minimum symptoms (reference group)	0.76	0.43	0	1
Mild	0.16	0.37	0	1
Moderate	0.060	0.24	0	1
Severe	0.018	0.13	0	1
Female	0.51	0.50	0	1
Age (in years)	21.0	1.85	18	25
Place of origin
Swiss (reference group)	0.52	0.50	0	1
Western Europe	0.35	0.48	0	1
Eastern Europe	0.030	0.17	0	1
Africa	0.073	0.26	0	1
Others	0.033	0.18	0	1
Education
Bachelor (reference group)	0.82	0.38	0	1
Master	0.16	0.36	0	1
Others	0.020	0.14	0	1
Family income
Less than USD 4000 (reference group)	0.081	0.27	0	1
(4000,7000]	0.21	0.41	0	1
(7000,12000]	0.34	0.47	0	1
More than 12000	0.26	0.44	0	1
Don’t know	0.10	0.30	0	1
School performance
Above average (reference group)	0.27	0.45	0	1
Average	0.60	0.49	0	1
Below average	0.13	0.34	0	1
Single (not in a relationship)	0.51	0.50	0	1
Close friends
None (reference group)	0.024	0.15	0	1
One	0.041	0.20	0	1
Two	0.16	0.37	0	1
Three or more	0.78	0.42	0	1
Siblings
None (reference group)	0.077	0.27	0	1
One	0.46	0.50	0	1
Two	0.31	0.46	0	1
Three or more	0.16	0.36	0	1
Relationship with parents
Good (reference group)	0.66	0.47	0	1
Good, but not always	0.31	0.46	0	1
Bad	0.031	0.17	0	1

Note: Unweighted sample characteristics of the students who have completed our online survey in April 2017.

Fig 1 shows the Epanechnikov kernel density of the self-assessed sleep difficulty of the college students in our sample. This distribution appears to be highly bimodal, with the middle inflection point at about 40. The majority of respondents in our sample appear to have mild sleep difficulties, where the density distribution is the highest at roughly 15. There is also a large share of our respondents who appear to have difficulties with their sleep, as evidenced by the large number of evaluations that are above 50.

Fig 1

Distribution of sleep difficulty evaluations.

Note: 0 means ‘no difficulty’ and 100 means ‘extreme difficulty’ with sleep.

Fig 2 reports the distributions of the five anchoring vignette evaluations. We can see that our five vignettes cover the range of possible sleep difficulty values very well. The first plot in the first row represents the evaluation by our respondents of the first vignette. There appears to be unanimity across our respondents: the sleep pattern of the fictitious person described in vignette 1 represents an ideal scenario (most of the density is located at 0). At the complete opposite, the middle plot in the second row represents the evaluation by our respondents of vignette 5. Although somewhat more skewed towards the left, most of our sample evaluated scenario 5 as representing the scenario of someone experiencing the most severe difficulty with one’s sleep pattern. Vignettes 2, 3, and 4 represent mid-range scenarios. It is interesting to note here that the evaluations of vignette 2 appear to be quite discordant, as revealed by the density which, in addition to displaying bimodality, is relatively high from value 20 to 70.

Fig 2

Distribution of vignette evaluations.

Note: 0 means ‘no difficulty’ and 100 means ‘extreme difficulty’ with sleep.

Relationship between depressive symptoms and sleep difficulties

We start our analysis by examining the bivariate relationship between self-assessed sleep difficulties and depressive symptoms. Fig 3 shows the levels of self-assessed sleep difficulties of respondents in our sample by depressive symptoms status. As can be seen from the densities, the bimodality of the distribution exists for all four depressive symptoms categories, although it is somewhat less pronounced for those who are moderately depressed and those who are severely depressed. The relationship between sleep difficulties and depressive symptoms is very strong: almost all individuals suffering from depressive symptoms, irrespective of the severity, have difficulties with their sleep, with the density shifting towards 100 the more severe the depressive symptoms are.

Fig 3

Distribution of sleep difficulty evaluations by depressive symptoms.

Note: 0 means ‘no difficulty’ and 100 means ‘extreme difficulty’ with sleep.

Results from a multivariate linear regression of self-assessed sleep difficulties measured from 0 to 100 on our set of control variables are reported in the first column of Table 2. Sex, age, income and relationship status appear to not affect sleep difficulties. Note that we report in the tables only the coefficients associated with sex, age, and depression symptoms status, as they are the main focus of this study. Details on the coefficient of the other variables are available upon request to the authors. Individuals suffering from ‘mild’, ‘moderate’ and ‘severe’ depressive symptoms however have experienced great difficulties with sleep as they have rated their sleep difficulties 20, 32, and 37 points higher, respectively, compared to college students with ‘no or minimal’ symptoms. These effects are all significant at the level of 1% (p<0.01).

Table 2

Linear regressions of sleep difficulties on our set of control variables.

	(1) Sleep difficulty	(2) Sleep difficulty	(3) Sleep difficulty	(4) Sleep difficulty	(5) Sleep difficulty	(6) Sleep difficulty
Female	1.24	1.58	1.29	1.62	0.87	0.21
	(1.20)	(1.18)	(1.21)	(1.20)	(1.14)	(1.09)
Age	0.20	0.078	0.16	0.20	0.13	0.14
	(0.39)	(0.38)	(0.39)	(0.39)	(0.37)	(0.36)
Mild depressive symptoms	19.6***	18.0***	19.7***	19.2***	15.6***	14.1***
	(1.69)	(1.67)	(1.69)	(1.68)	(1.66)	(1.57)
Moderate depressive symptoms	32.4***	30.8***	32.5***	31.2***	21.9***	24.7***
	(2.40)	(2.19)	(2.38)	(2.34)	(2.52)	(2.27)
Severe depressive symptoms	37.4***	35.7***	37.6***	36.8***	25.9***	28.5***
	(3.69)	(3.59)	(3.66)	(3.61)	(4.28)	(3.40)
Hours of sleep (reported)		-5.26***
		(0.59)
Hours of sleep (wake up time—bed time)			-0.77
			(0.56)
Hours of sleep, adjusted for time it takes to fall asleep				-2.95***
				(0.54)
Time to fall asleep (in hours)					25.8***
					(2.71)
Take more than 20 mins to fall asleep						17.7***
						(1.17)
Sleep less than 7 hours						6.76***
						(1.42)
Low sleep efficiency						9.07***
						(1.48)
Constant	17.5*	59.9***	24.6**	39.7***	9.68	11.9
	(9.93)	(10.9)	(10.6)	(10.5)	(9.88)	(9.18)

Note: Robust standard errors are in parentheses (* p < 0.1, ** p < 0.05, *** p < 0.01). We also control for parent’s income, education level, nationality, number of siblings, relationship status, relationship with parents, number of close friends and school performance. These coefficients are not reported in the table but are available upon request.

One may wonder whether the relationship between sleep difficulty and depressive symptoms could be confounded with sleep time and various patterns of sleep. Indeed, the association could be spurious if it turns out that sleep time or any other variables affecting both sleep difficulties and depressive symptoms are not controlled for in the analysis.

Columns 2, 3, 4, 5, and 6 of Table 2 however show that controlling for various measures of sleep patterns and efficiency that are commonly used in the literature does not critically affect the relationship between sleep difficulties and depressive symptoms. Descriptive statistics of these variables are presented in S1 Table. Controlling first for the reported effective hours of sleep of the respondents (column 2) [67, 75, 85, 86], which is derived from the question: Over the last month, how many hours of sleep have you had on average every night?”, one can see that the association between depressive symptoms and sleep difficulties remains very large and significant. For instance, the increase in sleep difficulties for those suffering from severe depressive symptoms, compared to those with no depressive symptoms, only changed from 37.4 points (p<0.01) to 35.7 (p<0.01). Controlling next for the hours of sleep defined as the difference between the time a person wakes up and the time he or she goes to bed [75], the effect of depressive symptoms again remains almost identical (column 3). In column 4, we control again for hours of sleep as defined in column 3, but this time correcting for the time it takes for respondents to fall asleep [75, 85]. Again the effect of depressive symptoms on sleep difficulties is very robust: for instance, the increase in sleep difficulties for those suffering from moderate depressive symptoms, compared to those with no depressive symptomts, only change from 32.4 points (p<0.01) to 31.2 (p<0.01), which corresponds to a change of only about 4%. The association also holds when we control only for the time it takes individuals to fall asleep instead (column 5) [67, 75, 87]. Two things are worth noting here. The first is that this variable captures some of the depressive symptoms-sleep difficulties gradients as the coefficients associated with depressive symptoms decreased by about 30%. Second, the time it takes individuals to fall asleep explains quite a lot of the sleep difficulties variation, “independently” of depressive symptoms status, given the large and statistically significant effect of the variable on sleep difficulties (about 25.8 points, p<0.01).

Finally, in column 6, we control for whether it takes more than 20 minutes for individuals to fall asleep (the usual cutoff point for sleep latency [2]) and whether college students sleep less than 7 hours per night on average [2]. In the same regression, we also add an indicator variable that reflects the sleep inefficiency of an individual as defined as taking the value of 1 if the ratio of the number of effective hours of sleep over the difference between the waking up time and the time the individual goes to bed is lower than 0.85 [75, 88–90]. Results show that including these three indicator variables in our statistical specification, although they are individually all positive and highly significant (p<0.01), do not appear to attenuate the associations between depressive symptoms and sleep difficulties.

Note that our results are robust to using PHQ-9 score as a continuous measure instead of descriptive depression categories. Indeed, as evidenced in S2 Table, the effect of a marginal increase in PHQ-9 score on sleep difficulty is equal to about 3 points (p<0.01) and remain positive and statistically significant even after including our various measures of sleep patterns and efficiency as control variables in the econometric specification.

Sleep patterns and hours of sleep, therefore, do not seem to explain the association between depressive symptoms and sleep difficulties as the association still appears to be strong and statistically significant after controlling for these different confounding variables. Could the association between depressive symptoms and sleep difficulties be explained, at least partially, by reporting heterogeneity? As explained above, individuals with depressive symptoms could report severe sleep difficulties, either because they are indeed deprived of good sleep as a result of depression or simply because they are apt to rate everything more negatively. Reporting heterogeneity could indeed stem from the fact that the meaning of the two end-points of our VAS, ‘no difficulty’, and ‘extreme difficulty’, could be interpreted very differently depending on whether a person suffers from depression or not. We now focus our analysis on reporting heterogeneity and try to answer this question.

Reporting heterogeneity in sleep difficulties

As we are most concerned about whether individuals with depressive symptoms could report sleep difficulty on a different scale from others, we start our analysis about the presence of reporting heterogeneity by exploring the bivariate relationship between vignette evaluations (which measure reporting scale) and depressive symptoms. Fig 4 shows the distribution of the evaluations of the five anchoring vignettes used in our study by depressive symptoms severity. If the vignette equivalence assumption holds, any difference in vignette evaluations by individuals with different depressive symptoms would suggest the presence of reporting heterogeneity in sleep difficulty assessment. The five plots of Fig 4 show that most vignette evaluations are relatively homogeneous, irrespective of the depressive symptoms college students are suffering from. This holds true except perhaps among those with severe depressive symptoms, for which noticeable differences can be seen in the evaluations of vignettes 2 and 4. While purely descriptive, this bivariate analysis already shed light on the possible presence of reporting heterogeneity in self-assessed sleep difficulty among college students with and without depressive symptoms.

Fig 4

Distribution of vignette evaluations by depressive symptoms.

Note: 0 means ‘no difficulty’ and 100 means ‘extreme difficulty’ with sleep.

We then resort to multivariate analysis and regress the five vignette evaluations on our set of control variables, including depressive symptoms. Under the vignette equivalence assumption, if the coefficient of a variable turns out to be statistically significant, then it would mean that the vignettes are not perceived equally by respondents who have the characteristic associated with that particular coefficient. In other words, there would be some reporting heterogeneity associated with that specific characteristic x (See Eq 6). Table 3 reports the results of the regressions of our five vignettes on our set of control variables. It is reassuring that very few coefficients are significantly different from 0, suggesting that individuals evaluate vignettes in a rather similar way. One exception clearly stands out, however. Individuals suffering from ‘moderate’ and ‘severe’ depressive symptoms appear to evaluate vignette 2 more negatively, with their evaluations being on average 8.3 (p<0.01) and 10.6 (p<0.05) points closer to ‘extreme difficulty’, respectively, compared to those with ‘no or minimal’ depressive symptoms. This suggests the presence of reporting heterogeneity in self-reported sleep difficulties in these two subgroups of individuals. College students with moderate depressive symptoms also tend to evaluate vignette 1 higher than college students without any depressive symptoms (6 points, p<0.05).

Table 3

Linear regressions of vignette evaluations on our set of control variables.

	(1) Vignette 1	(2) Vignette 2	(3) Vignette 3	(4) Vignette 4	(5) Vignette 5
Female	2.41**	0.48	-1.46*	-0.97	-1.67*
	(0.97)	(1.23)	(0.85)	(0.96)	(0.99)
Age	0.20	0.33	-0.25	-0.26	-0.26
	(0.31)	(0.39)	(0.28)	(0.31)	(0.31)
Mild depressive symptoms	0.87	-0.15	-0.91	-0.87	-1.51
	(1.29)	(1.67)	(1.11)	(1.31)	(1.38)
Moderate depressive symptoms	5.96**	8.26***	0.15	2.09	-3.34
	(2.78)	(2.62)	(2.17)	(2.19)	(2.56)
Severe depressive symptoms	-4.58	10.6**	3.76*	-1.32	1.92
	(3.17)	(4.37)	(2.25)	(3.19)	(3.78)
Constant	3.48	38.0***	66.7***	85.6***	95.0***
	(7.77)	(9.95)	(7.33)	(7.88)	(8.01)

Note: Robust standard errors are in parentheses (* p < 0.1, ** p < 0.05, *** p < 0.01). We also control for parent’s income, education level, nationality, number of siblings, relationship status, relationship with parents, number of close friends and school performance. These coefficients are not reported in the table but are available upon request.

Corresponding results when using PHQ-9 score instead of depressive symptoms as measure of mental health are presented in S2 Table. We show in the Appendix that PHQ-9 score has a statistically significant association with the evaluations of vignette 2 (0.55 points, p<0.01) but has no significant statistical correlation (at conventional level) with the evaluations of vignettes 1, 3, 4 and 5. These results are very much in line with results presented in Table 3.

To further determine the existence of reporting heterogeneity, we add vignette evaluations directly in the sleep difficulties regression as control variables. Indeed, assuming that individuals use the same reporting scale to evaluate their sleep difficulties as the scale they use to evaluate the vignettes, reporting heterogeneity can be directly controlled for by adding vignette evaluations as regressors in the econometric specification. Table 4 reports the results of these regressions. Column 1 is the result of regressing sleep difficulties on our set of control variables (same regression as column 1 of Table 2) and column 2 represents the results of the same regression including this time vignettes evaluations as control variables. Although vignettes 1’s and 2’s evaluations are themselves highly significant (0.10 points with p<0.01 and 0.09 points with p<0.01, respectively), the inclusion of vignettes as control variables does not affect the associations between depressive symptoms and sleep difficulties. The conclusion is identical when we add vignette evaluations (column 4) to the model that also controls for sleep patterns and efficiency (column 3). Our results are robust to using PHQ-9 score as a continuous measure instead of descriptive depression categories, as shown in S2 Table. These results indicate that the associations between sleep difficulties and depressive symptoms remain large and statistically significant even after controlling for reporting heterogeneity.

Table 4

Linear regressions of sleep difficulties on our set of control variables, including the vignette evaluations in columns 2 and 4.

	(1) Sleep difficulty	(2) Sleep difficulty	(3) Sleep difficulty	(4) Sleep difficulty
Female	1.24	1.08	0.21	0.053
	(1.20)	(1.19)	(1.09)	(1.08)
Age	0.20	0.18	0.14	0.12
	(0.39)	(0.39)	(0.36)	(0.36)
Mild depressive symptoms	19.6***	19.6***	14.1***	14.1***
	(1.69)	(1.70)	(1.57)	(1.57)
Moderate depressive symptoms	32.4***	30.9***	24.7***	23.2***
	(2.40)	(2.40)	(2.27)	(2.21)
Severe depressive symptoms	37.4***	36.8***	28.5***	27.9***
	(3.69)	(3.64)	(3.40)	(3.28)
Vignette 1		0.098***		0.10***
		(0.035)		(0.032)
Vignette 2		0.091***		0.088***
		(0.026)		(0.024)
Vignette 3		0.032		0.047
		(0.040)		(0.035)
Vignette 4		0.075*		0.072*
		(0.044)		(0.039)
Vignette 5		-0.0022		0.00078
		(0.044)		(0.041)
Take more than 20 mins to fall asleep			17.7***	17.7***
			(1.17)	(1.15)
Sleep less than 7 hours			6.76***	6.79***
			(1.42)	(1.41)
Low sleep efficiency			9.07***	9.15***
			(1.48)	(1.48)
Constant	17.5*	5.38	11.9	-1.21
	(9.93)	(10.4)	(9.18)	(9.68)

Note: Robust standard errors are in parentheses (* p < 0.1, ** p < 0.05, *** p < 0.01). We also control for parent’s income, education level, nationality, number of siblings, relationship status, relationship with parents, number of close friends and school performance. These coefficients are not reported in the table but are available upon request.

Because there nonetheless appears to be some reporting heterogeneity in self-assessed sleep difficulties, as evidenced by the statistically significant effect of some of our vignettes, it would be interesting to understand what factors drive this reporting heterogeneity. Since we observe both self-assessed sleep difficulties and vignette evaluations, we can run a double-index model that allows us to estimate the associations between our control variables and both sleep difficulties (free from any reporting heterogeneity) and reporting heterogeneity itself, hence enabling us to determine the factors explaining reporting heterogeneity.

Results from this model are summarized in Table 5. Odd-numbered columns represent the “true” associations between our control variables, net of any reporting heterogeneity (vector of coefficients b₀), and sleep difficulties, and even-numbered columns show the associations between our set of regressors and reporting heterogeneity (vector of coefficients γ). From column 1, it is clear that the associations between being mildly, moderately, and severely depressed and sleep difficulties remain very strong (with increases of 20.1, 29.8, and 35.3 points, respectively, compared to those with no depressive symptoms, all with p<0.01) and are very close to the ones obtained in column 2 of Table 4. The same is true when we include sleep patterns and efficiency in the model (column 3). Columns 2 and 4 show that individuals suffering from mild and severe depressive symptoms do not appear to evaluate the VAS scale differently from those with no depressive symptoms. Respondents with moderate depressive symptoms, however, do perceive the VAS scale differently, with their sleep difficulty evaluations being 2.6-2.7 points higher than what it “really should be”. That being said, this effect is very small, less than 10% in magnitude, and the associations between sleep difficulties and depressive symptoms remain very strong even after controlling for reporting heterogeneity. Again, these results are robust to using PHQ-9 score as a continuous measure instead of descriptive depression categories (S2 Table).

Table 5

Linear regressions of sleep difficulties on our set of control variables, accounting for reporting heterogeneity.

	(1) “True” effect b0	(2) Reporting Heterogeneity γ	(3) “True” effect b0	(4) Reporting Heterogeneity γ
Female	1.48	-0.24	0.42	-0.22
	(1.25)	(0.56)	(1.14)	(0.56)
Age	0.25	-0.049	0.19	-0.056
	(0.41)	(0.18)	(0.38)	(0.18)
Mild depressive symptoms	20.1***	-0.51	14.5***	-0.44
	(1.78)	(0.72)	(1.66)	(0.75)
Moderate depressive symptoms	29.8***	2.62**	22.0***	2.70**
	(2.60)	(1.32)	(2.43)	(1.35)
Severe depressive symptoms	35.3***	2.07	26.4***	2.12
	(3.85)	(2.20)	(3.56)	(2.21)
Take more than 20 mins to fall asleep			18.2***	-0.52
			(1.21)	(0.56)
Sleep less than 7 hours			6.46***	0.29
			(1.49)	(0.71)
Low sleep efficiency			9.05***	0.015
			(1.61)	(0.76)
Constant	17.5*		11.9
	(9.88)		(9.13)

Note: Cluster robust standard errors at the respondent level reported in parentheses (* p < 0.1, ** p < 0.05, *** p < 0.01). We also control for parent’s income, education level, nationality, number of siblings, relationship status, relationship with parents, number of close friends, and school performance. These coefficients are not reported in the table but are available upon request. Columns 1 and 3 show the effects of the control variables on sleep difficulties, net of reporting heterogeneity, while columns 2 and 4 show the effects of the control variables on reporting heterogeneity.