__Student Categorical
Proposal (Step 1):__

For
the final project in this class, I plan to write about some analyses that I
recently conducted using methods from this course. The purpose of the project
was to investigate the extent to which class and gender differences exist in
self-provisioning behavior, labor in which the laborer is simultaneously
producer and consumer. In particular, I tested the hypothesis that higher
levels of social status, operationalized in terms of income and business
ownership separately, predict less time spent self-provisioning in a variety of
domains. As a secondary hypothesis, I proposed that the well-established gender
differences in self-provisioning (e.g. Cast & Bird, 2007) would be
consistent across social strata. The
data for this project came from the American Time Use Survey (ATUS) and were
collected by the Department of Labor from 2003-2008 as a way of studying how
Americans spend their work and leisure time, I found support for both of my
hypotheses across a number of domains using a series of negative binomial
regressions and testing models testing these three predictors (i.e. wage,
business ownership, gender) and their interactions. For the purposes of this
project, I am also considering looking at certain domains in terms of either
the presence or absence of the activity (e,g.
mowing the lawn) and looking at these using the same predictors but in terms of
logistic regression.

__Professor Comments on
Proposal: __

This
sounds like it is on its way to being an excellent project. I can't completely
envision all your analyses, but it sounds like you are thinking about a whole
series of analyses. As it sounds like you are working towards a publication,
the series of analyses certainly will be sufficient for this class. I encourage
you to consider using this class project as a draft of your submission, rather
than just an step in-between the analyses and the
final paper that will be submitted. As you are using the negative binomial,
please be sure to check that the dispersion parameter warrants used of the
negative binomial rather than a Poisson distribution.

__Retrospective
Reflection:__

This proposal was somewhat incomplete but suggested
that an appropriate data set had been selected for the question being addressed.
Because of the size of the data set, it was clear that the student would have a
lot of flexibility in analysis, and if anything the challenge would be in
selecting a clear and concise set of analyses. Because there were relatively
few details about the planned analysis, it was difficult to know for sure that
the paper was on the right track, but the comments were intended to get the
student thinking about their analysis (negative binomial comments).

__Student Paper Draft
Excerpts (Step 2):__

[. . .]

Americans
also engage in *self-provisioning*:
labor for which the laborer is both producer and consumer. People grow their
own food in the garden, cook their own meals, do their own laundry, etc. In
short, there are three labor markets into which Americans invest time: 1)
Formal, or on-the-books, labor, 2) Informal, or
off-the-books, labor, and 3) Self-provisioning.

[. . .]

Specifically,
there are two primary research questions of interest. First, what is the
relationship between gender and class? Do the effects of gender remain consistent
across social classes in all domains? If not, of course, we will need to make
sense of those differences. Secondly, what is the relationship between social
class and self-provisioning? We have reason to believe that the relationship
between class and self-provisioning is somewhat complicated: sometimes we
expect wealth to reduce the time spent self-provisioning, but then there are
forms of self-provisioning that require immense wealth to do.

[. . .]

Methods

[. . .]

Results

[. . .]

*Cleaning, Laundry, and
Sewing *

For
this factor, and for all others, we have a DV that is a count variable (minutes
spent doing the task). We see that for this factor, however, a Poisson
distribution is not appropriate (*M* =
9.01, *SD* = 19.15). In fact, the AIC
for the full Poisson model is infinite, indicating that this is a poor choice.
For this factor, we used Negative Binomial regression, which allows us to
account for the overdispersion in the data[1].
Predicting minutes spent on this factor by gender, business, ownership, and
wage, we see a significant two way interaction we do
not see a three way interaction, but two significant two way interactions which
qualify our main effects.

First,
there is a significant interaction between gender and business ownership,
β = -.375, *z* = 4.23, p <
.0001. In particular, we see that for business owners, women are doing more
(β = 1.45, *z* = 18.57, p <.0001) and that this effect is in the same direction for
non-business owners (β = 1.08, *z*
= 36.92, p < .0001). The significant interaction suggests that the gender
gap is significantly smaller for non-owners.

There
is also a significant gender by income interaction (β = -1.23 x 10 -6, *z* = 2.56, p < .01). In particular, we
see that for men, income is not a significant predictor of the amount of time
spent on cleaning, laundry, and sewing, *z*
= .687, p > .49. For women, however, we observe the predicted effect of
wage, β = -8.33 x 10-7, *z* =
2.84, p < .01. For women, higher weekly income predicts less time spent on
cleaning, laundry, and sewing.

[. . .]

Discussion

[. . .]

As
a way of approaching these findings, I would like to propose a few clusters
that we should consider for the sake of clarifying these findings.

*Traditionally Feminine
Self-Provisioning*

Factors
1 and 2 have parallel results in the regression analyses above. These factors
include cleaning, sewing, laundry, cooking, and kitchen tasks. In short, these
are highly gendered tasks that are typically considered the domain of women's
work. We see, correspondingly, that women are doing much more of this work
compared to men.

Interestingly,
the gender gap is somewhat narrower for lower class (i.e. non-business owning)
respondents. This fits sociological analyses (Nelson & Smith, 1999) which suggest that in some ways, gender roles are a
luxury. If, for example, both partners in a household are working, then who does the cooking or laundry may depend more on who has
time and less on gender roles.

[. . .]

*Traditionally Masculine
Self-Provisioning*

We
also see that a few factors stand out as more common among men. In particular,
interior maintenance, vehicle maintenance, and appliance maintenance all have a
strong main effect for the gender of the participant. Fixing up around the
house and working on the car fall under traditionally masculine
self-provisioning.

With
regard to interior maintenance, we observe a main effect of wage such that
those who make more money spend more time engaged in interior maintenance. This
is perhaps due to the fact that wealthier individuals are more likely, for
example, to own a house and to be concerned with maintenance. Wealthier
individuals are presumably also more likely to own things that are worth
maintaining, whereas poorer individuals might rely on used goods or more
disposable products.

Wage,
however, has the opposite effect when it comes to vehicle repair and
maintenance. For men, we see that making more money means spending less time in
the garage. Wealthier men may prefer to hire out labor for auto repair by
taking broken vehicles to a mechanic or dealer, while others may try to save
money by doing this work for themselves. The effect may also be the result of
the kinds of cars that people are able to afford. Wealthier individuals are
going to have the money to buy newer cars that require less maintenance (and
still fall under warranty) whereas lower class individuals may depend more on
older used cars.

[. . .]

*High Investment
Self-Provisioning*

Some
forms of self-provisioning are only necessary because the people who engage in
them can meet the initial investments. For example, note that lawn and garden
care, pet care, and exterior maintenance all require serious investment. To be
able to garden, for example, one needs sufficient land and time. Likewise, it
takes considerable disposable income to afford one pet, let alone more than
one.

As
a result, we see that in general, for both men and women, owners and non-owners
alike, increased income predicts more time spent in high-investment
self-provisioning. Households that have more money potentially have more space
to garden, more pets in the house, bigger yards to mow, etc.

[. . .]

*Conclusions*

[. . .]

__Professor Comments on
Proposal: __

[. . .]

My
primary concern is that while the poisson
distribution or negative binomial distribution does seem to be appropriate
given the interval nature of the data, it seems likely that there is going to
be a larger preponderance of zeros in the data. While a larger percentage of
people may mow their lawn, on any given day it is unlikely that a person has mowed
their lawn. I suspect that the data consist of a large number of zeros,
followed by a distribution of remaining scores. It would be interesting to see
whether the pattern of results changes if one uses a method designed to model
the zeros differently from the other values, before fitting the models to the
non-zero values. A table indicating the percentage of people who gave non-zero
responses would also be helpful --- as this might call into question how much
can be inferred from these data. If only 20 people reported vehicle repair and
maintenance, we might not want to put much credit in the interpretation of the
results presented.

Minor
concerns & suggestions:

-The
author should address the practical significance of the results. Given the
large sample size, it is not surprising that significant p-values are very
small --- but in practical terms, how large are these effects? By how many
minutes do genders differ on these tasks? If we extrapolate out to a week, how
many more hours a week are women spending cleaning (for example)?

-Along
the same lines as the previous comment, it would also be helpful to rescale
predictors. For example, a 1 unit change in weekly
income is difficult to understand. It does a poor job of conveying the effect.
What are the effects for something like a $100 or $500 change in weekly income?

[. . .]

-Does
the survey include information about the number of hours individuals work
outside of the house? If so, the author needs to control for this information
--- someone who doesn't work outside of the house will probably do much of the
self-provisioning in the household. Furthermore, households with only one
income are likely to do much more self-provisioning to make ends meet.

-The
effect of income seems likely to be nonlinear. Please test the effect of a
linear and quadratic effect of income. Please include p-values indicating not
only the effects of the linear and quadratic components individually, but
tested simultaneously. That is, test the significance of including both effects
compared to a model without either effect, so as to get an impression as to
whether income as a whole is a useful predictor.

[. . .]

__Retrospective
Reflection:__

This
paper did an extensive number of analyses, as eight different areas of
self-provisioning behavior were examined. While the student put a lot of time into
completing each set of analyses for each of the eight sections and writing it
up, unfortunately there was a key issue with the analysis. The presence of
zeros in his data, bound to occur because people don't mow their lawn every
day, called into question the relationships that had been observed. While the
paper was also very complete in addressing statistical significance, it lacked
consideration of the practical meaning of the results. The paper was reasonable
at this stage, but would move into being excellent if these key issues were
addressed.

__Student Final Paper Excerpts --- Key
Changes (Step 3):__

[. . .]

Results

Prior
to analyzing time use spent self-provisioning, analyses should be run to verify
the predicted differences between gender and business ownership groups on
average weekly wage. Because the distribution of income is best fit by a Gamma
distribution (Salem & Mount, 1974; McDonald & Jensen, 1979), a GLM
function coding for business ownership, gender, and their interaction should be
modeledÉin a better version of this paper.

Turning
to the analyses of self-provisioning, we see a number of important findings
using our three predictors. I will discuss each factor separately below. The
purpose of these analyses is specifically to test the unique effects of gender
and social class, and hence time spent at work will be controlled throughout as
a covariate. To enhance the interpretability of the results, I have also
recoded wage by dividing by 100, thus all effects of wage will be reported in
units of 100 dollar per week increments.

*Cleaning, Laundry, and
Sewing *

For
this factor, and for all others, we have a DV that is a count variable (minutes
spent doing the task). We see that for this factor, however, a Poisson
distribution is not appropriate because the mean should approximate the
variance, but this is clearly not the case (*M*
= 36.05, *SD* = 76.61). As a result of
the overdispersion in these data, I will therefore
use negative binomial regression which can account for
this additional variability.

It
was also noteworthy that 64.51% of participants (31432 out of 48724) reported a
total of 0 minutes on cleaning, laundry, and sewing in the previous day. Given
that less than half of the sample has non-zero value for this count, it was
appropriate to use zero-inflated negative binomial regression, which models
specifically for those participants who have a count on this variable[2].

Specific
models were compared using a series of likelihood ratio tests. It was found
that the optimal model includes all main effects for gender, wage, and business
ownership as well as a gender x business owner interaction (and hours at work
as a covariate). This model was significantly better than the intercept only
model (*χ ^{2}*(10)
= 9542,

Once this was determined, a series of
models were estimated which included the main effect for a quadratic effect of
income, as well as possible interactions between the quadratic wage term,
gender, and business ownership. The optimal model in this case added a main
effect for the quadratic term as well as an interaction between gender and the
quadratic term to the previous model. This model was significantly better than
the model without quadratic terms for wage (*χ ^{2}*(4) = 96.23,

It
is worth noting that not all of the effects in this optimal model are actually
significant (see Table 1 for a summary). Notably, the gender x ownership
interaction (*z* = 1.95, *p* = .051) is only marginally
significant, and the interaction between gender and the quadratic term for wage
is also non-significant (*p* = .86). There are also no significant effects for the quadratic wage term (*p* = .13) nor for business ownership (*p* = .11).

The
only effects worth noting in the final model are a main effect for gender and a
main effect for wage. In particular we see that wage (in $100 per week
increments) is a significant predictor, *β*
= -.013 +/- .0067, *z* = 3.93, *p* < .0001. To put this into
perspective, someone making 100 dollars more than someone else will spend .98
(e ^{-.013}) times fewer minutes cleaning, doing laundry, and sewing.
At a gap of 500 dollars per week, this is a difference of .93 times, or the
difference of slightly more than four minutes per hour (60 * .93 = 55.8).

There
is also a significant effect for gender, *β*
= .2388 +/- .097, *z* = 4.84,* p* < .0001. As we might expect, women
are spending 1.27 times as many minutes cleaning, doing laundry, and sewing. In
terms of minutes, this means that a woman would be expected to spend 76.2
minutes (1.27*60) working at this task for every hour that a man spends.

[. . .]

Discussion

[. . .]

*Capital Required or
Class Advantage or Quadratic Effects?*

With
regard to social class, I suggested at least two ways we could think about the
relationship between social class and self-provisioning labor. Many forms of
self-provisioning labor require investments of capital to even make the labor
possible, as in the case of gardening, which requires both time and land.
However, for other forms of self-provisioning, such as cooking, it appears that
wealthier individuals should be expected to do less as they can afford, e.g. to
go to restaurants more often. Poorer individuals should be expected to
self-provision because this offers one concrete way of saving money (by
sacrificing time instead). It is cheaper to make a box of macaroni and cheese
than to order pizza, but the former takes more time than the latter.

Given
these two competing approaches to thinking about the relationship between
social class and self-provisioning, it seems reasonable to expect that perhaps
the effect of wage is quadratic. Perhaps as people make more money, they have
more access to domains of self-provisioning (e.g. pools to clean), but that
after a point, increased wealth leads to decreased
self-provisioning (e.g. as people hire someone to clean their pool). These
analyses attempted to test all three of these potential trends by looking for
simple directional effects of wage and business ownership, as well as quadratic
effects of wage within these data.

[. . .]

*Are** the Gender Gaps Stable Across Classes?*

Finally
I would like to return to the second research question behind this project: are
gender differences in self-provisioning stable across social classes? In
general, we see that the answer is yes: for a number of factors, there are main
effects of gender, but not significant interactions with either business
ownership or income.

In
particular, we see main effects of gender on a number of factors that are
traditionally gendered. Men spend more time engaged in vehicle repair and lawn
and garden work, and as we might expect, women spend more time cleaning and
cooking. Again, it is worth pointing out that cleaning and cooking behaviors
are far more common of course, and that the time use disparities here are by no
means equal over the long run.

There
are only two factors for which notable gender x class interactions arise.
First, with regard to cooking, we see that the gender gap is smaller between
business owning and non-business owning households. In both cases, women are
doing more of this essential, everyday labor, but the gap shrinks for lower
class families. This fits with analyses of self-provisioning practice that have
demonstrated the extent to which gender gaps are in some ways a luxury for
upper class families (Nelson & Smith, 1999). Poorer households may have,
for example, both partners of a heterosexual couple working, which may require
men to take up more of the cooking. Upper class households may have more
freedom to be single-earner households, and it is normative for the man in the
household to be that single-earner. This leaves cooking to the non-earning
partner: gender normatively this is the woman.

Secondly,
there is an interaction between gender and ownership with regard to exterior
maintenance (e.g. installing windows, cleaning the pool). In upper class
households, there is no gender gap for this form of labor, while we do see a
gap for lower class households (in which men are doing more of this sort of "handyman"
work). I attempted some post hoc analyses to suggest that the absence of a
gender gap among upper class families is the result of the fact that upper
class individuals regardless of gender are simply doing less exterior
maintenance. The gender gap here is that men are doing more, but specifically
lower class men. Again, we might expect that lower class men are motivated to
perform their own home repair and maintenance as a way to save money in a way
that upper class men are not.

*Conclusions*

[. . .]

__Retrospective
Reflection:__

In the revised paper, the student did an
extensive revision of the analysis, worked to consider the practical
significance of the results, and rewrote the discussion of the result to be
clearer and more in line with his questions of interest. These extensive
improvements led the paper to meet most of the requirements for an excellent
paper (see rubric). The student has since worked to revise the paper further
for publication.

[1] All of the analyses are conducted using Negative Binomial regression through the Zelig package (Imai, K., King, G. and Lau, O. (2007). "negbin: Negative Binomial Regression for Event Count Dependent Variables" in Kosuke Imai, Gary King, and Olivia Lau, "Zelig: Everyone's Statistical Software," http://gking.harvard.edu/zelig

[2] All zero-inflated-models were run using the zeroinfl command as part of the pscl package on R (Jackman, Tahk, Zeileis, Maimone, & Fearon, 2010).

[3] All non-zero-inflated models were run using Imai, K., King, G. and Lau, O. (2007). "negbin: Negative Binomial Regression for Event Count Dependent Variables" in Kosuke Imai, Gary King, and Olivia Lau, "Zelig: Everyone's Statistical Software," http://gking.harvard.edu/zelig