__Title__

**[U] 11.1.6 weight** -- Weights

__Remarks__

Most Stata commands can deal with weighted data. Stata allows four kinds
of weights:

1. **fweight**s, or frequency weights, are weights that indicate the number
of duplicated observations.

2. **pweight**s, or sampling weights, are weights that denote the inverse of
the probability that the observation is included because of the
sampling design.

3. **aweight**s, or analytic weights, are weights that are inversely
proportional to the variance of an observation; that is, the variance
of the jth observation is assumed to be sigma^2/w_j, where w_j are
the weights. Typically, the observations represent averages and the
weights are the number of elements that gave rise to the average.
For most Stata commands, the recorded scale of **aweight**s is
irrelevant; Stata internally rescales them to sum to N, the number of
observations in your data, when it uses them.

4. **iweight**s, or importance weights, are weights that indicate the
"importance" of the observation in some vague sense. **iweight**s have
no formal statistical definition; any command that supports **iweight**s
will define exactly how they are treated. Usually, they are intended
for use by programmers who want to produce a certain computation.

The general syntax is

*command* *...* **[***weightword***=***exp***]** *...*

For example:

**. anova y x1 x2 x1*x2 [fweight=pop]**

**. regress avgy avgx1 avgx2 [aweight=cellpop]**

**. regress y x1 x2 x3 [pweight=1/prob]**

**. scatter y x [aweight=y2], mfcolor(none)**

You type the square brackets.

Stata allows abbreviations: **fw** for **fweight**, **aw** for **aweight**, and so on.
You could type

**. anova y x1 x2 x1*x2 [fw=pop]**

**. regress avgy avgx1 avgx2 [aw=cellpop]**

**. regress y x1 x2 x3 [pw=1/prob]**

**. scatter y x [aw=y2], mfcolor(none)**

Also, each command has its own idea of the "natural" kind of weight. If
you type

**. regress avgy avgx1 avgx2 [w=cellpop]**

the command will tell you what kind of weight it is assuming and perform
the request as if you specified that kind of weight.

There are synonyms for some of the weight types. **fweight** can also be
referred to as **frequency** (abbreviation **freq**). **aweight** can be referred to
as **cellsize** (abbreviation **cell**):

**. anova y x1 x2 x1*x2 [freq=pop]**

**. regress avgy avgx1 avgx2 [cell=cellpop]**

__fweight____s__

Frequency **fweight**s indicate replicated data. The weight tells the
command how many observations each observation really represents.
**fweight**s allow data to be stored more parsimoniously. The weighting
variable contains positive integers. The result of the command is the
same as if you duplicated each observation however many times and then
ran the command unweighted.

__pweight____s__

Sampling **pweight**s indicate the inverse of the probability that this
observation was sampled. Commands that allow **pweight**s typically provide
a **vce(cluster** *clustvar***)** option. These can be combined to produce
estimates for unstratified cluster-sampled data. If you must also deal
with issues of stratification, see **[SVY] survey**.

__aweight____s__

Analytic **aweight**s are typically appropriate when you are dealing with
data containing averages. For instance, you have average income and
average characteristics on a group of people. The weighting variable
contains the number of persons over which the average was calculated (or
a number proportional to that amount).

__iweight____s__

This weight has no formal statistical definition and is a catch-all
category. The weight somehow reflects the importance of the observation
and any command that supports such weights will define exactly how such
weights are treated.

__Examples__

**. webuse hanley**
The next four commands are equivalent
**. roctab disease rating [fweight=pop]**
**. roctab disease rating [fw=pop]**
**. roctab disease rating [freq=pop]**
**. roctab disease rating [weight=pop]**

**. webuse total**
**. total heartatk [pw=swgt], over(sex)**

**. webuse byssin**
**. anova prob workplace smokes race workplace#smokes [aw=pop]**

**. webuse nhanes2f**
**. svyset psuid [pw=finalwgt], strata(stratid)**
**. svy: ologit health female black age c.age#c.age**
**. ologit health female black age c.age#c.age [iw=finalwgt]**