Consultation 2: A colleague of your professor has found out that your other professor is getting all this free advice from you and has subsequently sought you out for consultation. They are interested in understanding health expenditures of individuals on health promotion measures (or conversely disease prevention). They have a dataset of adults aged 40-60 years (N=467) that explores how education, SES, free time (non-work/non- sleeping hours) and age plays a role in these kinds of health expenditures. Their general model suggests health expenditures (HealthS) is a function of 1) knowledge about health which they equate to/measured by education- level in years (Educ); 2) resources to expend which they interpret as their SES measure (this is an index based on occupation and income-in SES units), 3) time resource (Time in hours free from work/sleep) since some promotion activities require time to commit to the activity (e.g. exercise), and 4) they control for age (in years) to account for different levels of "natural health" (younger people are typically healthier which may influence how much they feel a need to be invested in health promotion). This colleague has a pet argument that education's positive role in expenditure increases in its effect as people's SES increases (education is even more important to spending if you have higher SES compared to lower SES). They also were told by a friend to consider that free time as a resource may have a positive but a decreasing positive effect on expenditures. They send you an email with their results that attempt to capture the underlying view of health expenditures discussed above (especially accounting for their expectation about education's and SES's combined role and also accounting for free time. Below are some brief points they see in the interpretation of the model; the model is a continuous outcome (Health$) and they used a generalized linear model approach (i.e. maximum likelihood estimation). Comment on each point and provide guidance (including additional things they might try to address facets of the discussion above). You may also ask for more information to help you help them. You don't need to perform any calculations unless you think it will help explain your point. Be sure you assess their key interests in the research (i.e. are they doing what they intend to do). Means/s.d of the variables: Health$: 337 / 62 Age: Time: 49.5 5.3 4.8 2.9 SES: Education: 32.48.3 14.42.9 Iteration 0: log likelihood = -2521.3348 Generalized linear models Optimization Deviance : ML 1337696.718 Log likelihood = -2521.334783 No. of obs Residual df 467 461 BIC 1334863 | OIM health | Coef. Std. Err. Z P>|z| [95% Conf. Interval] age | 2.924 .4304 time .3972 1.358 time2| .8369 .3617 2.31 6.79 0.000 0.99 0.606 0.021 2.080 3.768 -2.303 3.097 .0709 1.546 educ | .9260 .4440 2.08 0.038 .0557 1.796 ses | 1.790 intercept | 95.33 .3958 26.41 4.52 0.000 3.61 0.000 1.015 2.566 43.55 147.1 NOTE: time2=time*time Test Ho: SES EDUC = 0 Likelihood Ratio y2 (df=2) = 38.2 Prob x2 0.0000 BICnull=60233 BICfull=49299 Dear Expert Grad Student: Given the regression model results shown above I am hoping to make the following points (see the 5 listed below). If I am wrong would you please indicate why and how I might address the kinds of questions I am asking ----i.e. I may not have written about the effect seen in the table correctly or maybe I didn't run the correct model to reflect what I really would like to say. Tell me if my model and various tests I performed reflect my interests---perhaps I have things in the model that are not necessary. I am comfortable with executing a multiple regression but if you think I should change the model please be explicit about what you want me to do. I have been told by my colleague you are quite helpful---and I'm in need of help! Thanks. 1) Controlling for all these variables the greater the SES of an individual the more they spend on Health; the confidence interval contains 1.79 so I am 95% confident that the marginal effect is 1.79. It is also the case that SES's effect is about twice as large as the effect of education. 2) It is also clear years of education is a positive effect (.926) and when people have both High Education with High SES this effect of education is even stronger on spending dollars on health. The difference in a model with and without the two variables, education and SES, shows they are important to the model fit. The LRX2 (2df) = 38.26 with a p-value of less than .0001 and the BIC value for the model is 49299 which is smaller than the BIC for the standard null model. 3) I did expect free time to have a positive effect and see it is but it is weak and not distinguishable from zero (i.e. the 95% interval is at the low end negative and at the upper end positive). However, the square of free time works as expected. This seems to capture what my colleague suggested would be the effect of time. Clearly as Time increases spending increases by .836 (it doesn't seem to decrease as he thought it would). 4) Clearly Age (net of the other variables) is what drives spending compared to the other variables. The older you are the stronger the effect of age is on health spending. 5) Yesterday I showed a colleague these results and they wondered if an elasticity model would work better instead of my quadratic model to capture the relation between expenditures and free time---I am not sure what he meant or if that would, if fact, be better. How do you do this elasticity model and given my current results do you think it would be worth trying? Any help would be appreciated!!! I'll cite you with a big thank you in a footnote once this is published. (Hint: there may be some value in you stating what the basic systematic equation is from the table of results... then address whether the professor is correct in their interpretation and has successfully addressed the key or "pet" points that they wanted make. Writing out the equation for the estimated model and what you see as the model discussed at the beginning might be useful, too. Some simple calculations may prove useful, too.)