Modeling errors in surveys with overlapping panels
Definition
The following concepts are required to define a rotating panel:
| Concept | Definition | Symbol |
|---|---|---|
| Base frequency | Frequency of the model latent variables (e.g. months, quarters) | $t$ |
| Survey period | Number of periods (in the base frequency) during which the survey continiously takes place | $lag$ |
| Stint | Division of the survey period (e.g. week). Each individual is surveyed always at the same stint of the survey period | $t_j$ |
| Wave | The $i$th wave comprises a group of individuals that have been surveyed for the $i$th time | waves $1,\ldots,i,\ldots, W $ |
| Persistence | The total number of waves or, equivalently, the number of consecutive survey periods that a first wave individual will remain in the panel | $W $ |
| Wave-specific error | For a given wave, the difference between the average response and the actual perception (subset of the wave corresponding to base period $t$) | $e^{(i)}_t$ |
| Bias term | Part of the wave-specific error that accumulates over the survey period (it is assumed to be zero on average for all waves) | $b^{(i)}_t$ |
| Correlation term | Part of the wave-specific error at time $t$ that is independent from the bias component, and may be correlated with the error at time $t-lag$ | $\epsilon^{(i)}_t$ |
jd3_ssf_msae
This R function is used to define an error structure corresponding to a rotating panel. The error model belongs to the JD+ class JD3_SsfItem
output
Object of the JD+ class JD3_SsfItem:
usage
jd3_ssf_msae(name, nwaves, ar, fixedar=TRUE, lag=1)
| Argument | Definition | Default | Remarks |
|---|---|---|---|
| name | string with the name of the component | ex. "errorStructure", do not forget the commmas | |
| nwaves | integer representing the number of waves | The first wave contains individuals that have been surveyed for the first time. The second wave contains the individuals that have been surveyed for the second time. The last wave corresponds to the individuals that have been surveyed for the last time (they will not participate in the survey again). Note that the rotating panel design ensures that all individuals are interviewed only once in the same survey period and this happens always at the same stint (e.g. week). | |
| ar | R matrix representing the covariance structure of the wave specific survey error. | FALSE | The input matrix is conformed with the rows of the upper triangular matrix that represents the correlation structure in a compact manner (see example below for $W=5$ and $nlags=3$). It is possible to select the first row ($\phi^{2}_{1},\phi^{3}_{1},\phi^{4}_{1},\phi^{5}_{1}$), the first two rows, or the entire matrix. The zeroes in the first column do not appear in this input matrix |
| fixedar | logical that triggers the estimation of the correlation patterns (TRUE) or fixes them to the values given by the entries of the input matrix above (FALSE) | TRUE | |
| lag | integer specifying the number of time periods (in the base frequency) that compose the survey period. This coincides with the number of time periods an individual has to wait between two different waves. Note that if the survey period is one quarter, all of them have already responded in the previous wave exactly 3 months ago (because individuals are always interviewed at the same stint during each survey period). | 1 |