Table 1.
Equations in the human-built model. The concepts in the Concept column are from the schematic in Figure 3. These equations contain unobserved parameters (highlighted in bold) which modify the effects of social role mechanisms. These are given values following model calibration (Section 3.3) which searches for the set of parameters which best fit historically observed trends in alcohol use over time. The agents in the model, indexed by i, represent individual drinkers; their behaviour is a decision to consume the jth drink in a drinking occasion. The model also includes two dynamic structural entities: expectancies for holding roles at a given point in the lifecourse and average transition probabilities (TP) between roles. For clarity, all structural entities carry the prefix s. The discrete time unit (representing each day) in the simulation is k.
| No. | Concept | Model equation | Description |
|---|---|---|---|
| 1 | Role strain | RoleStraini[k] = (RoleLoadi[k] + RoleIncongruencei[k]) / 2 | Role strain is the overall stress an individual experiences as a result of the social roles they hold. |
| 2 | Role load | RoleLoadi[k] = β1*ParentStatusi[k]*ParentInvolvementi + β2*MaritalStatusi[k]*MaritalInvolvementi + β3*EmploymentStatusi[k]*EmploymentInvolvementi + β4*(1-MaritalStatusi[k])*ParentStatusi[k]*ParentInvolvementi | Role load is the stress that results from needing to perform a role. Role status is either 0 (not having a role) or 1 (having a role). Role involvement represents how much a person is involved in a role, if they hold it (between 0 and 1, from no involvement to full involvement). There are four terms: one term for each of the three roles (having a role and more involvement in that role increases the stress) and a term for additional stress when an individual is a single parent (holding the role without the support of another parent). |
| 3 | Role incongruence | RoleIncongruencei[k] = (ParentStatusi[k]-sParentExpectancysex,age[k] + MaritalStatusi[k]-sMaritalExpectancysex,age[k] + EmploymentStatusi[k]-sEmploymentExpectancysex,age[k]) / 3 | Role incongruence is the stress that results from holding a role that deviates from societal expectations for an individual’s identity (encoded as a sex-age category). It is the average of the differences for each role between the current status and the corresponding societal expectancy (prevalence of that role in the society is between 0 and 1). |
| 4 | Role transition update for gaining roles | Heavy drinkers:
|
To account for role selection, individual role transitions over the lifecourse are calculating by modifying the societal transition rates according to whether or not the individual is a heavy drinker. (Equation 4 and 5). Heavy drinking makes it less likely for an individual to gain roles. Heavy drinking makes it more likely for an individual to lose roles. AnnualHeavyDrinkingPrevalence represents the population prevalence of heavy drinking in the model (between 0 and 1) |
| 5 | Role transition update for losing roles | Heavy drinkers:
|
|
| 6 | Difference in disposition to drink due to gaining roles | DispositionDifferencei,j[k] = Dispositioni,j[k]*(1+β10) - Dispositioni,j[k] | To account for role socialization, the disposition to drink is gradually reduced the longer an individual holds a role and is gradually increased if an individual loses a role. The full disposition effect to apply is calculated using Equation 6 or 7. The proportion of that effect to apply after a particular number of days of socialization is calculated using the logistic function in Equation 9. This modifier is then applied to scale the full disposition effect using Equation 8 and calculate the overall disposition at time k. Socialisation effects accrue over one year following a role transition. |
| 7 | Difference in disposition to drink due to losing roles | DispositionDifferencei,j[k] = Dispositioni,j[k]*(1+β11) - Dispositioni,j[k] | |
| 8 | New disposition to drink (after role socialisation) | Dispositioni,j[k]=Dispositioni,j[k-1] + DispositionDifferencei,j[k]*modifieri[k] | |
| 9 | Modifier for socialisation mechanisms | modifieri[k] = e^((DaysofSocialisationi[k]-sSocialisationSpeed)/365) / (1+e^((DaysofSocialisationi[k]-sSocialisationSpeed)/365)) | |
| 10 | Opportunity to drink out | logOddsOppOuti[k] = log(β5*(1 - β6*RoleLoadi[k] + β7*EmploymentStatusi[k])) | Equation 10 and 11 describe the log odds for the opportunities to drink outside and inside the home, with reference to having no opportunity to drink. β5 is the baseline opportunity. Role load acts to reduce both opportunities. Individuals have more opportunity to drink outside the home if employed, and more opportunity to drink inside the home when holding marital or parenting roles. Equation 12 and 13 operationalize the logit model that derives the probabilities of drinking outside and inside the home on any given day from the log odds of Equation 10 and 11 (for three mutually exclusive scenarios: drinking in, drinking out, and not drinking). |
| 11 | Opportunity to drink in | logOddsOppIni[k] = log(β5*(1 - β8*RoleLoadi[k] + β9*(MaritalStatusi[k] + ParentStatusi[k]))) | |
| 13 | Probability of having an opportunity to drink out | probOppOuti[k] = e^(logOddsOppOuti[k]) / ((e^(logOddsOppIni[k])+e^(logOddsOppOuti[k])+1)) | |
| 12 | Probability of having an opportunity to drink in | probOppIni[k] = e^(logOddsOppIni[k]) / ((e^(logOddsOppIni[k])+e^(logOddsOppOuti[k])+1)) | |
| 14 | Probability of drinking first drink (j=0) | ProbabilityDrinki,0[k] = Dispositioni[k] * (ProbOppOuti[k]+ProbOppIni[k]) * (1+β14*RoleStraini[k]) | The daily drinking probability is modelled as the long-term drinking disposition, mediated by drinking opportunities and role strain. We differentiate between drinking frequency (first drink in an occasion) and quantity (next drink, given that an occasion has begun). |
| 15 | Probability of drinking next drink (j>0) | ProbabilityDrinki,j[k] = Dispositioni[k] * (ProbOppOuti[k]+ProbOppIni[k]) * (1+β15*RoleStraini[k]) | |