# Convenience and data sufficiency square6 what

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Convenience and data sufficiency square6 what functional forms will be convenient to use computationally, or are just simple to write out and explain? square6 for what functional forms can I estimate the parameters easily with the available data?

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13 Alternative Models of Risks Functional Reasonableness square6 Does the selected functional form generate values of the dependent variable y in the physically reasonable range? square6 Does the model allow the dependent variables x, w and z to take on values in their physically reasonable range? square6 Does the selected functional form for the model capture the likely qualitative character of the relations among x,w,z and y when each variable is changed separately while holding the others constant as well as when several vary together? Linear Model of Death Rate Y (deaths per mile, per year, per hour) Y=a+bX+cW+dZ Where X,W, and Z reflect exposure levels to different death causing agents. This makes sense if the three causes of death act independently and in particular if the effects of changing one variable is independent of the level of the others. For example the deaths per year due to motor vehicle accidents could reasonably be described by X= number of under 25 year old male drivers, W=number of under 25 year old female drivers, and Z= number of over 25 drivers. If a-d are all + and the exposure levels are all +, then only + death rate Y will result. However, if exposure to some agent X decreases the death rate then enough of this agent could result in an unrealistic negative Y.
14 Multiplicative model with continuous variables Y=dX a W b Z c Where X,W, and Z are continuous variable describing exposure levels. The result of exposure from X on Y can be nonlinear,where a determines whether Y increases like the square or the square root of X. Moreover the impact of the different factors is multiplicative, so that each either enhances or diminishes the level of Y established by the other factors. Factor model with binary variables Y=da X b W c Z Where X,W, Z are zero-one variables reflecting absence or presence of a factor. A good model when the presence or absence of each factor X,W and Z enhances or depresses the level of Y established by the other factors. This may result from a chain of events. For example, driving drunk may triple ones accident rate while wearing a seatbelt results in a 40% reduction in fatalities in accidents that occur so that a=0.4 and X=1 for with seatbelt and X=0 otherwise. Likewise if drunk driving triples chance of an accident then b=3 and W=1 if drunk and 0 otherwise. This functional form generates values of Y 0

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15 Probabilistic fatality model Y=100,000[1-s(1-aX)(1-bW)(1-cZ)] =100,000[1-s(1-a) X (1-b) W (1-c) Z ] Where X,W, Z are zero-one variables reflecting absence or presence of a factor each of which affects survival in a multiplicative way. Here Y is the death rate per 100,000 and s(1-aX)(1-bW)(1-cZ) is the probability of surviving the independent attack of agents X,W, and Z; s is background survival probability reflecting all other causes of death. If each survival probability is between zero and one, then 0 s(1-aX)(1-bW)(1-cZ) 1 and 0 Y 100,000 Probabilistic fatality model Y=100,000[1-s(1-aX)(1-bW)(1-cZ) =100,000[1-s(1-a) X (1-b) W (1-c) Z For small a,b, and c the probabilistic fatality model reduces to the linear model for death rates: Y=100,000[(1-s)+s(aX+bW+cZ)]
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• Spring '10
• fernando
• Evans, air travel, fatality rate

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