Thanks again for joining us in Course 6 which is

called 'Combining and Analyzing Complex Data'.

It's taught by me,

Richard Valliant, and Frauke Kreuter.

So you'll be seeing both of us in this course.

We're into Module 2 now which has to do with estimating model parameters.

So we, in the previous module,

we talked about estimating simpler things like means and totals but

we're now going to move onto these more complex S demands.

Now, because we're dealing with a finite population,

it's good to think about what exactly is happening here.

So, one way to think about the whole process is - suppose there's

an underlying super population model up here

that is really what we're trying to discover or to estimate.

And that populate, that model,

generates a finite population

so we get realizations from that model that creates the finite population.

From the finite population, we draw our sample,

and then from the sample, we fit a model.

Now what is this fitted model estimating?

As shown here, we can think of it two ways.

If we've got the model specified just right,

it agrees with the super population model then that fitted model

will be estimating this super population model,

the thing that started the whole process.

On the other hand, if we misspecify the model a bit,

say we leave out some covariates or something,

we didn't know about them.

What we are gonna be able to say is the fitted model still

is aiming at the best fitting model for the whole finite population.

So it may be misspecified in the sense that we left out

a covariate or something that was in the super population model.

But, we're still doing a pretty good job at aiming at the full finite population model.

Now, another way to think about that for finite population model is,

it's the model that you would fit if you

had the entire population in hand, in your sample.

So, for that reason it's often called the census model.

You know that's the thing that we're aiming at when we go through

the fitting algorithms as we'll show you in a bit.

So, one thing that is true and is, you know,

kind of a source of debate in finite population estimation is,

if the same model is appropriate for the sample as for

the full pint, the full population,

you don't have to use the weights, any way,

this would be true if your sample is a little miniature, the full population.

But if you've done something to kind

of throw the sample off balance compared to the population,

say you targeted some subgroups or you've used

PPS sampling so you tend to see the biggest units more often in your sample,

then this may not be true.

And to get back to estimating that census model,

you're going to need the weights.

Now, another thing that you need to account for is

stratification in clustering in your sample design,

because those will affect standard errors.

You know, they may make them either bigger or smaller but they'll definitely have

an effect and you can't ignore that.

So, we're going to use the weights in our procedure

and that means that definitely we'll be aiming at that census model.

If we work hard to specify our model correcty, the census model,

will also be the same form as

the super population model that we hope underlies the whole process.

So we'll see some examples of how to go about this in the next videos.