1 Motor vehicle crashes are a leading cause of death and injury for children under 8 years . While 2 different states are showing increase s in the proportion of child restraint device use, only around half 3 of the children aged between 4 to 7 years are being properly restrained . This study w as undertaken 4 to identify the factors contributing to the proper child restraint use and child passenger’s seating 5 position through the direct observation surveys of more than 10,000 child passengers in 2015 and 6 2018 in Michigan . A bivariate probit model was developed to simultaneously identify the 7 contributing factors for the proper restraint use and seating position of child passengers . The bivariate 8 framework is able to account for correlation of the two dependent variables in the study . The results 9 show that the two dependent variables are positively correlated , and this correlation is strongly 10 significant. Also, the key factors simultaneously influencing proper child restraint use and 11 appropriate seating position of the child passenger include the age of the child, number of the child 12 passengers in the vehicle, driver belt use , driver gender, age , and race, vehicle type , stratum, weather, 13 and the time of the day and week. However, factors such as county -specific population, income, and 14 education, and the type of location did not have a significant association with either child restrain t 15 use or the seating position of the child passenger. 16 17 Keywords: Child Restrain t Device Use, Seating Position , Child Passenger Safety , Bivariate Probit 18 Model 19 Chakraborty, Mahmud, and Gates 3 INTRODUCTION 1 Motor vehicle crashes are a leading cause of death and injury for children under 8 years of age in 2 the U.S. (1). Nationwide, between 2014 and 2018, a staggering total of 304,803 children under the 3 age of 8 years died or suffered from vehicle occupant injuries (2). During the same time, only in 4 Michigan, 72,094 children aged less than 8 years were involved in motor vehicle crashes combining 5 all severities. This was a sharp increase ( greater than 70 percent) from the number of children 6 under the age of 8 years involved in traffic crashes between 2009 and 2013 (3). In Michigan, 7 among the child occupants under the age of 8 years for whom restraint use in formation was 8 recorded, less than 73 percent used child -specific restraint, either a child restraint device (CRD) or a 9 belt-positioning booster seat (3). Data also shows that about 35 percent of the children , who died in 10 a traffic crash , were not restrained in 2017 in the U.S. (4). At the state level, among the children 11 aged less than 8 years that were either unrestrained or improperly restrained in Michigan , almost 5 12 percent suf fered fatal or incapacitating injuries (3). This was significantly higher than the children 13 who sustained fatal or incapacitating injuries but were properly restrained (0.12 percent ) (3). 14 Over the past two decades, Michigan has experienced increases in the use of CRD among 15 children under 4 years of age from 74.5 percent in 1997 to 98.2 percent in 2018 (5). On the other 16 hand, following the en actment of statewide legislation in 2008, booster seat use was found to 17 increase substantially in Michigan (5, 6). However, despite these increase s in CRD use, even less 18 than 55 percent of children aged between 4 and 7 years used booster seats properly (5). Research 19 has also demonstrated that children between the ages of 4 and 8 years are the least likely to be 20 protected in the appropriate restraint (7–9). There are several potential explanations for the low 21 booster seat use rate, including a lack of knowledge of the state law and best practice regarding the 22 benefits of child appropriate restraints compared to seatbelts alone, as well as differences in risk 23 perception among parents (10–13). 24 Children should be strapped in appropriate restraints based on their age, weight , or height. 25 Michigan’s Child Passenger Safety Law requires infant and convertible safety seats for children 26 under the age of 4 and booste r seats for children aged 4 until they fit in a seatbelt , which is usually 27 at the age of 8 or 9 years (5, 14). Research has clearly shown that the appropriate use of CRDs and 28 booster seats can significantly reduce the risk of serious injury and death for children involved in 29 vehicle crashes. Child safety seats reduce fatal injury by 71 percent for infants (under 1 year old) 30 and by 54 percent for toddlers (1 to 4 years old) in passenger vehicles (15). The risk of serious 31 injury for children 1 to 4 years old is 80 percent lower for children seated in forward -facing CRDs 32 than children restrained in merely safety belts (16). Also, b ooster seat use reduces the risk for 33 serious injury by 45 percent for children aged between 4 and 8 years, when compared with seatbelt 34 use (17). 35 While the extant literature provides important insights into the child restraint use and the 36 safety benefits of the proper restraint use , literature assessing proper use of restraint use 37 simultaneously with the seating position of the child is scant. To this end, this study examines the 38 factors that are associated simultaneously with appropriate child restraint use and proper seating 39 position of the child passenger . The data was collected from 263 sites in 30 counties across 40 Michigan in 2015 and 2018 as part of direct observation surveys. Data including the type of 41 restraint use, drivers’ demographic characteristics, and vehicle type along with county -level socio - 42 demographic information were obtai ned in the process of data collection. The appropriateness of 43 the restraint use was defined based on the child’s age and the c orresponding restraint use type. 44 Similarly, the seating position is defined as appropriate, if the child was placed in a rear se at. 45 46 47 Chakraborty, Mahmud, and Gates 4 LITERATURE REVIEW 1 Prior studies have established that sitting in the rear seat of a vehicle is safer than sitting in the front 2 seat in the event of a crash, and that the child safety seats perform better at reducing injuries (18– 3 21). While some studies have separately examined the sitting behavior and restraint use among 4 child passengers and have identified common risk factors for both these variables (22–24), some 5 other studies have also found a significant relationship between the two variables (25–27). Using 6 Fatality Analysis Reporting System (FARS) (28) data, a study determined that both child restraint 7 use and rear seating were associated with statistically significant reductions in the likelihood of a 8 child dying in a crash (29). Despite concerns around the sitting be havior and low restraint use 9 among child passengers, few studies assessed the child restraint use and child’s seating 10 appropriateness simultaneously. However, if the interrelationship between a child’s restraint use 11 and sitting position is due to unobserv able characteristics of the driver and the child passenger, then 12 analyzing these two variables separately may produce bias estimates (30, 31). A recent study from 13 Ghana investigated sitting behavior and restraint use among child passengers and clearly indicated 14 the existence of interrelat ionship between child passenger s’ seating position and restraint use. The 15 key factors simultaneously influenc ing child passenger’s sitting position and restraint use included 16 vehicle type, driver’s gender, driver’s belt use, child’s age, and the presence of other child or adult 17 passenger. Also, the time of the day, and the day of the week influence only the chil d’s sitting 18 behavior. Female drivers were less likely to position child passengers at the front seat and were 19 more likely to restrain them. However, the age of the driver and the gender of the child did not 20 have a significant effect on either the child’s seating position or the restraint use (32). 21 Existing research indicates that various sociodemographic, and vehicle characteristics are 22 associated with the likelihood of using CRDs. Robinson et al. (2002) found that both ethnicity and 23 parent age were significantly related to knowledge of neonatal car seat location. Results of their 24 study indicated that African American parents and parents aged less than 22 years were least likely 25 to know the correct child restraint use and seating position (33). Miller et al. (1998) reported that 26 more children were found unrestrained if the driver was male, young, a drinking driver, and 27 traveling at night (34). Conversely, a few other studies indicated that male drivers are more likely 28 to properly restrain the child in a vehicle than their female counterparts (11, 13, 35). Agran et al. 29 (1998) analyzed the restraint use of children aged under 9 years in fatal crashes and determined 30 negative associations between child restraint use, and the age of children, number of vehicle 31 occupants, older and larger vehicles, traveling during 3:00 AM to 6:00 AM , and traveling in rural 32 areas. Driver res traint use was found to be the strongest predictor of child restraint use, and 33 unrestrained and young (less than 18 years old) drivers were associated with lower restraint use of 34 child passengers (36). In an interview -based study in Australia, Keay et al. (2013) showed that the 35 inappropriate and non -use of restraint among children aged between 2 to 5 years were more likely 36 when the driver was less than 36 years old, had a family with three or more children, or from a 37 family where a language other than English was spoken at home (37). 38 A study from Michigan found that the highest number of children aged between 4 and 8 39 years riding completely unrestrained (44 percent) were those traveling in passenger vehicles . With 40 unrestrained drivers, more than 90 percent of the children were riding completely unrestrained . 41 Moreover, m iddle -aged drivers (30 to 59 years) had the highest rate of proper booster seat use (35). 42 A similar study determined that the restraint use was low for older children in both pickup trucks 43 and passenger cars (38). The strongest factor identified by a study tha t influenced child restraint 44 use was the age of the child with the younger child being restrained more often. The other factors 45 leading to increased child restraint use included cases where the driver was white, the parent was 46 the driver, and there were t hree or fewer occupants in the vehicle. Interestingly, no significant 47 Chakraborty, Mahmud, and Gates 5 relationships were fou nd between the parent's age and the frequency of restraining the child (39). A 1 study by Rangel et al. (2008) determined that the lowest rate of proper restraint use was among 4 to 2 8 year old children. The likelihood of any type o f restraints being used was 2.3 times higher for 3 Caucasian children than African American children. The compliance with restraint laws a mong 4 African American children remains significantly lower than even the national average (40). A 5 cross -sectional study in Iran showed the prevalence of child safety seat use was significantly 6 associated with higher income among parents (41). In a study designed to investigate child safety 7 seat knowledge in post -partum mothers, Spanier et al. (2002) determined that the higher level of 8 educ ation the mother had attained, the more knowledge she had regarding child passenger safety. 9 Also, African American mothers and mothers from lower socioeconomic statuses performed worse 10 on child passenger safety questions. However, this relationship seeme d to be related to the 11 education level in their study (42). 12 For most studies, driver restraint use was identified as one of the key predictors for child 13 restraint use (42, 43). Macy and Freed (2012) determined that the unrestrained drivers and 14 traveling in a passenger car were predictors of a lower likelihood of CRD use. Addi tionally, 15 children riding with a younger driver had lower odds of booster seat use. However, the child’s and 16 driver’s gender were not associated with appropriate restraint use (44). Glassbrenner (2003) 17 showed that when a driver is restrained, child passengers are restrained 92 percent of the time 18 compared to 72 percent of the time when drivers are not restrained (45). However, a confounding 19 study showed that there were no significant relationships between booster sea t use and parental 20 characteristics including parent’s age, education level, and their self -reported seatbelt use (46). 21 To summarize, several of these studies have attempted to determine child restraint usage 22 rates, and the safety benefits of CRDs and booster seats. Yet there remains a dearth of research that 23 simultaneously analyzes the appropriate child restraint use and proper seating position of the child 24 passenger in motor vehicles. To address this knowledge gap, this study develops bivariate probit 25 models to estimate the two variables simultaneously using the data from direct observation surveys 26 in Michigan in 2015 and 2018. 27 28 29 METHODOLOGY 30 31 Site Selection 32 Study locations were selected to obtain CRD and booster seat use data from a representat ive sample 33 of target -aged (0 to 7 year -old) child passengers in the state of Michigan . The specific observation 34 sites were selected from a statewide sample of locations expected to yield high volumes of target - 35 aged child passengers, including fast food restaurants, daycare centers, shopping centers, and 36 recreational sites (e.g., zoos, museums, parks, etc.) . Ultimately, a total of 263 sites in 30 different 37 counties in Michigan were selected for data collection . The candidate counties were also classified 38 into four strata based on the past safety belt use rates and vehicle miles traveled (VMT) (31). 39 Stratum 1 consists of the counties with the highest historical safety belt use rates while Stratum 4 40 has exhibited the lowest belt use rate . Figure 1 shows the strata of the counties and the data 41 collection locations. To allow for a direct comparison between the results of these surveys, the 42 same sites were utilized each year , where feasible. 43 44 Chakraborty, Mahmud, and Gates 6 1 FIGURE 1: Data collection locations in different counties in Michigan 2 3 4 Data Collection 5 Data collection was performed by trained observers who received both classroom and field training 6 before the actual observation survey . The observers positioned themselves on the roadside near the 7 entrance or exit to each study location as vehicles would be either stopped or slowly moving 8 ensuring a clear line of sight into the interio r of each vehicle . At the primary observation sites 9 where traffic volumes were relatively low, data were also collected from vehicles on the adjacent 10 street . For all vehicles identified to have a 0 to 7 year -old child passenger, the driver and all target - 11 age child passengers were observed for restraint use and non -use. A sample field observat ion form 12 is shown in Figure 2 . During the direct observation use surveys, several factors were assessed as 13 part of the data collection including vehicle type (passe nger vehicles, sport utility vehicles (SUVs) , 14 vans/minivans, or pickup trucks); driver restraint use, gender, age group and ethnicity; and child 15 restraint use, age , and seating position . Driver restraint use was categorized as belted, not belted, or 16 unknown . The seven restraint categories for each child were: belted, not belted, unknown, rear - 17 facing child safety seat, front -facing child safety seat, high -back booster, or backless booster. 18 19 Chakraborty, Mahmud, and Gates 7 1 FIGURE 2 Data collection from 2 3 4 Statistical Methodology 5 This study analyzes the factors that are associated with proper child restraint use and proper seating 6 position of the child passenger simultaneously . Because the dependent variables consist binary 7 indicator variables (i.e., the child passenger was proper ly restrained or not , and the seating position 8 was appropriate or not ), discrete outcome models are an appropriate analysis framework. Given 9 concerns as to potential correlation between these two variables of interest , bivariate probit models 10 are well sui ted to the context of this study. The bivariate probit models were developed to account 11 for the common unobserved factors that are simultaneously associated with the proper child 12 restraint use and seating position of a child passenger . The bivariate prob it regression is an 13 extension of the univariate binary probit regression and is designed to model two binary dependent 14 variables that may be simultaneously estimated (47). A bivariate probit model essentially discounts 15 the correlation between the disturbances resulting in inefficiency in model estimations when the 16 univariate probit models are separately developed (48). The generic form of a bivariate probit 17 model can be expressed as: 18 𝑦1𝑖∗=𝛽1𝑋1𝑖+ 𝜀1𝑖 (1a) 19 𝑦2𝑖∗=𝛽2𝑋2𝑖+ 𝜀2𝑖 (1b) 20 where 𝑦1𝑖∗ and 𝑦2𝑖∗ are latent dependent variables; 𝛽1 and 𝛽2 are the vectors of estimable parameters; 21 𝑋1𝑖 and 𝑋2𝑖 are the vectors of explanatory variables; 𝜀1𝑖 and 𝜀2𝑖 are the disturbance terms assumed 22 to be normally distributed with mean and variance are 0 and 1 respectively, and correlation of ρ. 23 Dependent variables 𝑦1 and 𝑦2 are observed if the latent var iables 𝑦1∗ and 𝑦2∗ are greater than 0: 24 𝑦1=1, if 𝑦1∗>0, 0 otherwise (2a) 25 𝑦2=1, if 𝑦2∗>0, 0 otherwise (2b) 26 The parameters of the bivariate probit can be estimated by maximum likelihood with the log - 27 likelihood function expressed as (30): 28 𝑙𝑛 𝐿=ƩlnФ2[𝑞1𝑖 𝛽1𝑋1𝑖,𝑞2𝑖 𝛽2𝑋2𝑖,𝑞1𝑖 𝑞2𝑖 𝜌] (3) 29 Chakraborty, Mahmud, and Gates 8 where ( Ф2[𝑋1,𝑋2,𝜌) is the cumulative density function for the bivariate standard normal 1 distribution with correlation ρ; such that 𝑞1𝑖 =2𝑦1𝑖−1; and 𝑞2𝑖 =2𝑦2𝑖−1. Hence, 𝑞𝑗𝑖 =1 if 2 𝑦𝑗𝑖=1 and 𝑞𝑗𝑖 =−1 if 𝑦𝑗𝑖=0 , for j = 1, 2. 3 The correlation coefficient , rho (ρ), estimates the correlation between correct child restraint 4 use and correct seating position of a child passenger after the effects of the independent variables in 5 the model are accounted for. In the model results, the sign of the parameter estimat es (𝛽s), exhibits 6 the effect of each variable on both child restraint use and seating position of the child . A positive 7 parameter implies that the factor would increase the likelihood of proper restraint use or proper 8 seating position of a child passenge r and vice versa. 9 10 Preliminary Analysis 11 The statewide child restraint device use survey was performed between June and August of 2015 and 12 2018 . During this observation period, a total of 12,567 observations of 0 to 7 year -old child 13 passengers were obtained . Data were screened for missing values in different categories and a total 14 of 10,137 complete observations were tabulat ed for further analysis . County -level demographic data 15 including population, education level , and median household income were further added to the final 16 data set . Descriptive statistics of the child restraint use survey are provided in Table 1. 17 For the purpose of this study, the “appropriate” child restraint use was defined based on the 18 current Michigan law enacted in 2008 (49). Thus, the proper restraint for the children under the age 19 of 4 years were children seated in a rear -facing or forward -facing chil d safety seat . Premature 20 graduation to a booster seat or safety belt was classified as inappropriate restraint use for this age 21 group . Similarly, appropriate restraint use for children ages 4 through 7 years included forward - 22 facing restraint or booster s eat (high back or backless) . Premature graduation to safety belts 23 without a booster was classified as inappropriate . Proper seating position was defined when the 24 child was seated on the middle or back rows of a car, and conversely, when the child was sea ted at 25 the front seat , it was considered an improper seating position. 26 The preliminary analysis in this study reveals that, 27  The proper CRD use rates were 97.2 percent and 61.5 percent for children up to 3 years and 28 4 to 7 years, respectively, indicating a much lower CRD use rate for children aged 4 years or 29 older. 30  Only a small number of children were improperly seated (front s eat), approximately 0. 4 31 percent and 6.2 percent for children under 3 years and 4 to 7 years, respectively. 32  Approximately, in one third of the observations, there were multiple child passengers in the 33 vehicle. 34  Overall, more than 97 percent of drivers were found to be properly belted and majority of 35 the drivers were male . While the middle -aged (30 to 59 years) drivers account for almost 36 three -quarter of the sample, followed by the young drivers (16 to 29 years), only less than 5 37 percent of the drivers were old (above 60 years). Also, majority of the drivers was white. 38  Among the different vehicle types, passenger cars were most commonly observed, followed 39 by SUVs and van/minivans, and lastly pickup trucks. 40  With regard to the loc ation types, shopping centers and fast food restaurants were most 41 commonly observed . Moreover, these locations have comparable representations from all 42 four strata. 43  Lastly, majority of the observations were obtained during clear weather, during the 44 weekd ays, and in the morning s. 45 46 47 Chakraborty, Mahmud, and Gates 9 TABLE 1 Descriptive Statistics (n = 10,137 ) 1 Factor Frequency Percentage Factor Frequency Percentage Child Restraint Use Vehicle Type Proper use 7,947 78.4 Passenger car 4,529 44.7 Improper use 2,090 21.6 Sport utility vehicle 3,395 33.5 Child Seating Position Van or minivan 1,702 16.8 Proper 9,802 99.7 Pickup truck 511 5.0 Improper 335 0.3 Location Type Child Age Shopping 4,245 41.9 Under 2 years 1,598 15.8 Fast Food 3,056 30.1 2 to 3 years 3,471 34.2 Recreation 2,119 20.9 4 to 7 years 5,068 50.0 Daycare 717 7.1 Number of children Geographic Location One child 6,603 65.1 Stratum 1 2,439 24.1 Multiple children 3,534 34.9 Stratum 2 3,282 32.4 Driver Belt Use Stratum 3 2,328 23.0 Driver belted 9,913 97.8 Stratum 4 2,088 20.6 Driver not belted 224 2.2 Weather Driver Gender Clear 8,823 87.0 Male 8,718 86.0 Light fog/rain 1,314 13.0 Female 923 9.1 Day of the week Driver Age Weekend 1,796 17.7 Under 30 2,344 23.1 Weekday 8,344 82.3 30 to 60 7,295 72.0 Time of the day Over 60 498 4.9 Morning 5,238 51.7 Driver Race Afternoon 4,899 48.3 White 8,718 86.0 African American 923 9.1 Asian/ Hispanic/others 496 4.9 2 3 4 RESULTS AND DISCUSSION 5 For this study, all observations , where at least one child passenger is present along with the driver 6 in a motor vehicle , were analyzed. A total of 10,137 such observations were analyzed a fter 7 removing all unknown data . As the likelihood of proper child restraint use (age-appropriate) is not 8 independent of the likelihood of proper seating position (rear/middle seat) of the child passenger , it 9 is important to understand this correlation between the se two variables . Hence, to analyze the 10 factors that simultaneously affect both proper ch ild restraint use and proper seating position of the 11 child passenger, a bivariate probit model was developed wherein the information related to the child 12 passenger as well as the driver were included along with v ehicle - and site -related factors . The 13 depen dent variables in all models are coded as a binary indicator implying proper and improper 14 child restraint use and child passenger’s seating position . The regression analysis in this study was 15 carried out using R Studio . 16 Table 2 displays the results of t he final bivariate probit model for both the dependent 17 variables . The independent variables in all models included child passenger’s age, number of child 18 passengers in the ve hicle, driver’s age, gender, race, vehicle type, strata, weather, time of the day , 19 and day of the week , each statistically significant at a 90 percent confidence level for predicting 20 either child restraint use , or child’s seating position , or both . County -specific socioeconomic 21 Chakraborty, Mahmud, and Gates 10 factors including population, income, and education level did not have any s ignificant association 1 with either of the dependent variables and hence were further removed from the models. A 2 significance level of 0.1 was used in this analysis. 3 As shown in Table 2, the results displayed comparable parameter estimates for most of the 4 independent variables in child restraint use and child seating position models . The correlation 5 parameter ( ρ = 0.7002, p -value <0.001) is large and statistically significant, indicating the presence 6 of common unobserved factors that may affect the proper use of child restraint and seating position 7 of the child passenger. Also, t he correlation coefficient is positive, indicating the use of proper 8 child restraint is more likely to have the correct seating position of the child passenger as well. This 9 finding is important and consistent with previous literature that identified a correlation between 10 child passenger’s restraint use and seating position (32). 11 12 Child Restraint Use 13 As can be seen from Table 2, the results reveal several interesting findings. First, the likelihood of 14 proper child restraint use significantly reduces as the child’s age increases, especially when the 15 child is between 4 to 7 years old. This agrees with findings from other studies that determined a 16 higher likelihood of proper restraint use for younger children compared to those 4 years or older 17 (27, 50). Moreover, having more than one child passenger in the vehicle increased the likelihood 18 that the child would be properly restrained, although this association is not statistically significant. 19 Similar to previous studies (24, 32, 44), the child is more likely to be properly restrained if the 20 drive r of the vehicle is properly belted. While middle -aged (30 to 59 years) drivers are found to be 21 more likely to properly restrain the child passenger compared to the young drivers (16 to 29 years), 22 old drivers are least likely to use the child restraint pr operly. This could be due to the fact that 23 elderly drivers traveling with child passengers are likely to be the grandparents of the child. As 24 grandparents are typically not the child’s primary care -giver, it could be possible that they migh t 25 not have ade quate information on a CRD, and that may have resulted in low rate of correct 26 installations. 27 Contrary to the general consensus that females are more responsible towards their children, 28 the results of this study show that male drivers are more likely to pro perly restrain the child 29 passenger, a finding that is consistent with multiple previous studies (11, 13, 35), although this 30 association is not statistically significant. The white drivers are most likely to properly use the 31 child restraint compared to its African American counterparts or drivers of other races. Drivers of 32 passenger vehicles are the least likely to restrain their children properly, which has also been shown 33 in other studies (44, 50). Conversely, drivers of vans/minivans were the most likely to properly 34 install their child passengers. Drivers in stratum 1, where historically driver’s seat belt use is the 35 highest in the state, are most likely to properly restrain the child passenger. On the other hand, 36 drivers in stratum 4, which comprises of highly populated locations, are least likely to use the child 37 restraint properly. Furthermore , the likelihood of proper child restraint use increases in light fog or 38 rain compared to clear weat her conditions. Finally, the use of proper restraint use for child 39 passenger is higher over the weekends and in the afternoons. 40 41 Child’s Seating P osition 42 For child’s proper seating position in terms of being seated in middle or rear seats, the age of th e 43 child is negatively associated with the proper seating position of the child passenger, implying that 44 the higher the age of the child passenger is, the lower is the likelihood of the child being properly 45 seated. Similar to the child restraint use, havin g more than one child passenger in the vehicle 46 increased the likelihood that the child would be properly seated . Moreover, a properly belted driver 47 Chakraborty, Mahmud, and Gates 11 significantly increases the likelihood of the child being properly positioned in the vehicle. Unlike 1 the u se of child restraint, driver age did not significantly influence the seating position of the child 2 passenger. Furthermore, male drivers are more likely to properly position a child passenger 3 compared to their female counterparts. Similar to child restra int use , white drivers are most likely 4 to place the child passenger correctly compared to drivers of other races . The proper seating of a 5 child passenger is the least in pickup trucks and most likely in passenger cars. Additionally, the 6 likelihood of pos itioning the child passenger in the rear or middle seats is the highest in stratum 1, 7 followed by strata 4, 3, and 2, respectively. The proper seating positioning increases during light 8 fog or rain compared to clear weather. Also , the proper placing of a child passenger is greater 9 during the weekends and in the afternoons. Lastly, the high correlation between the child 10 passenger’s seating position and the restraint use indicates that a child properly seated in a car is 11 highly likely to be correctly restrained. 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Chakraborty, Mahmud, and Gates 12 TABLE 2 Results of Bivariate Probit Models for Drivers and Passengers (n = 10,137) 1 Parameter Proper child restraint use Proper child seating Estimate Std. Error z- value p- value Estimate Std. Error z- value p- value Intercept 1.939 0.167 11.63 <0.001 2.867 0.284 10.1 <0.001 Child age = up to 2 years Baseline Baseline Child age = 2 to 3 years -0.892 0.130 -6.85 <0.001 -0.276 0.215 -1.28 0.199 Child age = 4 to 7 years -2.439 0.125 -19.5 <0.001 -1.441 0.201 -7.16 <0.001 Number of children in the vehicle = 1 Baseline Baseline Number of children in the vehicle > 1 0.018 0.036 0.49 0.621 0.607 0.070 8.72 <0.001 Driver belt use = Not properly belted Baseline Baseline Driver belt use = properly belted 0.552 0.097 5.71 <0.001 0.357 0.162 2.21 0.027 Driver age = 16 to 29 years Baseline Baseline Driver age = 30 to 59 years 0.072 0.042 1.7 0.089 0.048 0.072 0.66 0.509 Driver age = 60+ years -0.018 0.083 -0.22 0.824 0.221 0.137 1.61 0.106 Driver gender = Male Baseline Baseline Driver gender = Female -0.027 0.037 -0.73 0.467 -0.187 0.068 -2.73 0.006 Driver race = White Baseline Baseline Driver race = Black -0.317 0.056 -5.68 <0.001 -0.129 0.105 -1.22 0.221 Driver race = Other -0.256 0.073 -3.53 <0.001 -0.103 0.124 -0.83 0.405 Vehicle type = Passenger car Baseline Baseline Vehicle type = SUV 0.347 0.039 8.93 <0.001 -0.156 0.070 -2.22 0.027 Vehicle type = Van/minivan 0.674 0.053 12.63 <0.001 -0.124 0.090 -1.38 0.168 Vehicle type = Pickup truck 0.065 0.074 0.88 0.379 -1.023 0.093 -11.03 <0.001 Stratum 1 Baseline Baseline Stratum 2 -0.164 0.048 -3.39 <0.001 -0.324 0.088 -3.69 <0.001 Stratum 3 -0.161 0.052 -3.12 0.002 -0.273 0.089 -3.09 0.002 Stratum 4 -0.169 0.051 -3.33 <0.001 -0.183 0.093 -1.97 0.048 Weekday Baseline Baseline Weekend 0.178 0.045 3.97 <0.001 0.104 0.073 1.42 0.155 Weather = Clear Baseline Baseline Weather = Light rain or fog 0.663 0.057 11.6 <0.001 0.405 0.099 4.1 <0.001 Time of the day = Morning Baseline Baseline Time of the day = Afternoon 0.114 0.035 3.26 0.001 0.016 0.060 0.27 0.789 Rho ( 𝝆) 0.7002 0.027 26.67 <0.001 Number of observations 10,137 Log-likelihood -4691.612 2 3 In addition to the model estimated parameters ( β) for each independent variable, the 4 marginal effects for each variable are also of interest. The marginal effects provide a means of 5 examining the magnitude of the effect of each independent variable on proper child restraint use or 6 proper seating position of the child passenger in the context of the observed data collected for this 7 study. Table 3 provides the marginal effects for the bivariate probit model including the estimates 8 Chakraborty, Mahmud, and Gates 13 and their corresponding p -values. The marginal effects for each independent variable are also 1 comparable between the two dependent variables, although, the extent or magnitude of these effects 2 vary between the child restraint use and seating position. 3 4 TABLE 3 Marginal Effects of Pr edictors (n = 10,137) 5 Parameter Proper child restraint use Proper child seating Estimate p-value Estimate p-value Child age = 2 to 3 years -0.165 <0.001 -0.005 0.186 Child age = 4 to 7 years -0.450 <0.001 -0.025 <0.001 Number of children in the vehicle > 1 0.003 0.621 0.011 <0.001 Driver belt use = Not properly belted 0.102 <0.001 0.006 0.030 Driver age = 30 to 59 years 0.013 0.089 0.001 0.513 Driver age = 60+ years -0.003 0.824 0.004 0.107 Driver gender = Female -0.005 0.468 -0.003 0.005 Driver race = Black -0.059 <0.001 -0.002 0.222 Driver race = Other -0.047 <0.001 -0.002 0.404 Vehicle type = SUV 0.064 <0.001 -0.003 0.029 Vehicle type = Van/minivan 0.125 <0.001 -0.002 0.160 Vehicle type = Pickup truck 0.012 0.379 -0.018 <0.001 Strata 2 -0.030 <0.001 -0.006 <0.001 Strata 3 -0.030 0.002 -0.005 0.004 Strata 4 -0.031 <0.001 -0.003 0.058 Weekend 0.033 <0.001 0.002 0.164 Weather = Light rain or fog 0.122 <0.001 0.007 <0.001 Time of the day = Afternoon 0.021 0.0011 0.0003 0.7892 6 7 8 CONCLUSIONS 9 This study simultaneously analyzes the factors that are associated with the child restraint use and 10 seating position of child passengers of motor vehicles . For this study, the analysis was carried out 11 on the data that has been collected from 263 sites across 30 counties in Michigan in 2015 and 2018 12 as part of direct observation surveys. The categories for the child restraint use included in this 13 analysis were properly restrained indicating age -appropriate child restraint use , and not properly 14 restrained that includes using some restraint but not child restraint device (CRD) . Similarly, the 15 other dependent variable was the proper seating position, which is essentially the rear or middle 16 seats of the vehicle, and improper seating position implying the front seats. Additional data 17 consi dered in this analysis included child passenger’s age, number of child passengers in the 18 vehicle, driver’s age, gender, and race, vehicle type, strata, weather, time of the day, and day of the 19 week. 20 Overal l, a total of 10,137 observations were analyzed where at least one child passenger was 21 present in a vehicle. A bivariate probit model was developed that simultaneously estimated both 22 the use of CRD as well as the seating position of the child passenger in a vehicle. The use of the 23 bivariate model accounts for the correlation between the two dependent variables and provides 24 increased efficiency compared to the separate univariate probit models. The correlation parameter 25 (ρ) of the final bivariate model was found to be large and highly significant implying the presence 26 of common unobserved factors affecting the use of child restraint as well as the seating position of 27 Chakraborty, Mahmud, and Gates 14 the child passenger . Also, the positive correlation parameter indicated that the proper use of CRD 1 is more likely to have the child passenger correctly seated in the vehicle and vice versa. 2 Factors including child’s age, the number of child passenger in a vehicle, driver’s age, 3 gender, and race, vehicle type, strata , weather, time of the day, and day of the week were all found 4 to be significantly associated with either child restraint use, or child’s seating position, or both . In 5 general, the effects of different factors associated with the two dependent variables were mostly 6 similar. County -specific socioeconomic factors including population density, income, and 7 education level did not have any significant association with proper child restraint use and child’s 8 proper seating position. 9 The results reveal that the proper child restraint use, and proper child seating position are 10 less likely with the increase in age of the child passenger. When more than one child is present in 11 the vehicle the likelihood for proper restraint use and seating of a child passenger is greater, and this 12 is particularly significant for the appropriate seating position of the child. Young driver s are, in 13 general, found to be least responsible in using proper child restraint or placing the child in the 14 correct seats. While male driver s were more likely to use the CRD and place the child correctly , 15 white drivers were found to be most likely to do the same. Also, proper child restraint use was least 16 likely in passenger vehicles, but it is more common to have the child correctly seated i n passenger 17 cars. Furthermore, the proper use of child restraint and seating position of the child passenger is 18 most likely in stratum where the occupant seatbelt use is historically the highest in the state. Lastly, 19 for both the dependent variables, tra veling in light rain or fog, in weekends , and in the afternoons 20 increased the like lihood of proper use of CRD as well as proper placement of the child passenger in 21 a motor vehicle . 22 Overall, the results of this study support the previous research findings and provide more 23 evidence that the interaction of various demographics, vehicle, and site -related characteristics are 24 significantly associated with the use of CRD and the seating position of the child passenger , in 25 addition to. More importantly, the stud y contributes to the limited body of knowledge regarding the 26 correlation between CRD use and child passenger’s seating position. 27 28 ACKNOWLEDGMENT 29 The study utilized the data collected for a project supported and funded by Michigan Office of 30 Highway Safety Planning (OHSP). OHSP disclaims any liability, of any kind, or for any reason, 31 that might otherwise arise out of any use of this publication or t he information or data provided in 32 the publication. 33 34 AUTHOR CONTRIBUTION STATEMENT 35 The authors confirm contribution to the paper as follows : study conception and design: Meghna 36 Chakraborty, Timothy Gates ; analysis and interpretation of results: Meghna Ch akraborty , Md. Shakir 37 Mahmud ; draft manuscript preparation: Meghna Chakraborty , Md. Shakir Mahmud, and Timothy 38 Gates . All authors reviewed the results and approved the final version of the manuscript. 39 40 41 42 43 44 45 46 47 Chakraborty, Mahmud, and Gates 15