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Clarinetist
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This is a follow-up to the question How to approach time data that aren't time series?.

I realized that my prior question was missing an important nuance, so I have to change the hypothetical scenario entirely.

Imagine the following scenario: suppose I, as a researcher, hypothesize that teachers who have more experience teaching tend to give their students more As. As with the prior question, significance tests and effect sizes are desired. Because teachers have to receive certification to teach through obtaining an academic degree, I suspect that there's an association between how long ago a teacher graduated from their certification program, and the rate at which teachers issue As to their students out of all students taught so far.

You may assume that I have available the following in a data set: points $\{(u_i, t_i, \mathbf{y}_i)\}_{i=1}^{N}$ where

  • $u_i$ is the unique identifier for a teacher
  • $t_i$ is the year at which the teacher graduated from their certification program
  • $\mathbf{y}_i = (y_{1i}, y_{2i})$ is a vector consisting of two components for each teacher: the count of As ($y_{1i}$), and the count of grades that are not As ($y_{2i}$) since the teacher graduated from their certification program.

Like with the prior question, I don't think this is a time series problem, but upon re-reading the prior answer, I don't think this is a panel data or longitudinal data problem either. We run, however, into similar problems to the ones I pointed out in the prior question:

  • We don't have an equal number of teachers in each year for which teachers graduate.
  • If my sample is insufficient so that some calendar years were skipped, I will have data for some calendar years but not for others, breaking the usual "equal-spacing" assumption with time series.
  • The data are probably not stationary if we were to consider using the graduation year as an index for time.
  • We could attempt to bin graduation years together, but such a mechanism has no precedent (i.e., assume no similar study has been done), and would be quite arbitrary to implement.
  • Given $t_i$, we also suspect that $\sum_{\{i : u_i \text{ graduated in year }t_i\}}\dfrac{y_{1i}}{y_{1i} + y_{2i}}$ (the rate at which As were given) would be similar for values of $t_i$ that are close to each other, so any binning of graduation years we do would ignore this to an extent that I would not be comfortable with without adequate justification.

Additionally, there's an aspect of this that should be controlled for: teachers who have graduated at an earlier year naturally have higher counts in $\mathbf{y}_i$ than those who graduated at a later year.

I suspect this is more complex than viewing this as a time series or longitudinal data problem. What technique(s) would you suggest for approaching this problem?

EDIT: As mentioned in the comments, assume all $\mathbf{y}_i$ are gathered at the same time and that all teachers in the data are still employed at this institution.

This is a follow-up to the question How to approach time data that aren't time series?.

I realized that my prior question was missing an important nuance, so I have to change the hypothetical scenario entirely.

Imagine the following scenario: suppose I, as a researcher, hypothesize that teachers who have more experience teaching tend to give their students more As. As with the prior question, significance tests and effect sizes are desired. Because teachers have to receive certification to teach through obtaining an academic degree, I suspect that there's an association between how long ago a teacher graduated from their certification program, and the rate at which teachers issue As to their students out of all students taught so far.

You may assume that I have available the following in a data set: points $\{(u_i, t_i, \mathbf{y}_i)\}_{i=1}^{N}$ where

  • $u_i$ is the unique identifier for a teacher
  • $t_i$ is the year at which the teacher graduated from their certification program
  • $\mathbf{y}_i = (y_{1i}, y_{2i})$ is a vector consisting of two components for each teacher: the count of As ($y_{1i}$), and the count of grades that are not As ($y_{2i}$) since the teacher graduated from their certification program.

Like with the prior question, I don't think this is a time series problem, but upon re-reading the prior answer, I don't think this is a panel data or longitudinal data problem either. We run, however, into similar problems to the ones I pointed out in the prior question:

  • We don't have an equal number of teachers in each year for which teachers graduate.
  • If my sample is insufficient so that some calendar years were skipped, I will have data for some calendar years but not for others, breaking the usual "equal-spacing" assumption with time series.
  • The data are probably not stationary if we were to consider using the graduation year as an index for time.
  • We could attempt to bin graduation years together, but such a mechanism has no precedent (i.e., assume no similar study has been done), and would be quite arbitrary to implement.
  • Given $t_i$, we also suspect that $\sum_{\{i : u_i \text{ graduated in year }t_i\}}\dfrac{y_{1i}}{y_{1i} + y_{2i}}$ (the rate at which As were given) would be similar for values of $t_i$ that are close to each other, so any binning of graduation years we do would ignore this to an extent that I would not be comfortable with without adequate justification.

Additionally, there's an aspect of this that should be controlled for: teachers who have graduated at an earlier year naturally have higher counts in $\mathbf{y}_i$ than those who graduated at a later year.

I suspect this is more complex than viewing this as a time series or longitudinal data problem. What technique(s) would you suggest for approaching this problem?

This is a follow-up to the question How to approach time data that aren't time series?.

I realized that my prior question was missing an important nuance, so I have to change the hypothetical scenario entirely.

Imagine the following scenario: suppose I, as a researcher, hypothesize that teachers who have more experience teaching tend to give their students more As. As with the prior question, significance tests and effect sizes are desired. Because teachers have to receive certification to teach through obtaining an academic degree, I suspect that there's an association between how long ago a teacher graduated from their certification program, and the rate at which teachers issue As to their students out of all students taught so far.

You may assume that I have available the following in a data set: points $\{(u_i, t_i, \mathbf{y}_i)\}_{i=1}^{N}$ where

  • $u_i$ is the unique identifier for a teacher
  • $t_i$ is the year at which the teacher graduated from their certification program
  • $\mathbf{y}_i = (y_{1i}, y_{2i})$ is a vector consisting of two components for each teacher: the count of As ($y_{1i}$), and the count of grades that are not As ($y_{2i}$) since the teacher graduated from their certification program.

Like with the prior question, I don't think this is a time series problem, but upon re-reading the prior answer, I don't think this is a panel data or longitudinal data problem either. We run, however, into similar problems to the ones I pointed out in the prior question:

  • We don't have an equal number of teachers in each year for which teachers graduate.
  • If my sample is insufficient so that some calendar years were skipped, I will have data for some calendar years but not for others, breaking the usual "equal-spacing" assumption with time series.
  • The data are probably not stationary if we were to consider using the graduation year as an index for time.
  • We could attempt to bin graduation years together, but such a mechanism has no precedent (i.e., assume no similar study has been done), and would be quite arbitrary to implement.
  • Given $t_i$, we also suspect that $\sum_{\{i : u_i \text{ graduated in year }t_i\}}\dfrac{y_{1i}}{y_{1i} + y_{2i}}$ (the rate at which As were given) would be similar for values of $t_i$ that are close to each other, so any binning of graduation years we do would ignore this to an extent that I would not be comfortable with without adequate justification.

Additionally, there's an aspect of this that should be controlled for: teachers who have graduated at an earlier year naturally have higher counts in $\mathbf{y}_i$ than those who graduated at a later year.

I suspect this is more complex than viewing this as a time series or longitudinal data problem. What technique(s) would you suggest for approaching this problem?

EDIT: As mentioned in the comments, assume all $\mathbf{y}_i$ are gathered at the same time and that all teachers in the data are still employed at this institution.

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Clarinetist
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Time data that aren't time series - except now, consider a duration aspect

This is a follow-up to the question How to approach time data that aren't time series?.

I realized that my prior question was missing an important nuance, so I have to change the hypothetical scenario entirely.

Imagine the following scenario: suppose I, as a researcher, hypothesize that teachers who have more experience teaching tend to give their students more As. As with the prior question, significance tests and effect sizes are desired. Because teachers have to receive certification to teach through obtaining an academic degree, I suspect that there's an association between how long ago a teacher graduated from their certification program, and the rate at which teachers issue As to their students out of all students taught so far.

You may assume that I have available the following in a data set: points $\{(u_i, t_i, \mathbf{y}_i)\}_{i=1}^{N}$ where

  • $u_i$ is the unique identifier for a teacher
  • $t_i$ is the year at which the teacher graduated from their certification program
  • $\mathbf{y}_i = (y_{1i}, y_{2i})$ is a vector consisting of two components for each teacher: the count of As ($y_{1i}$), and the count of grades that are not As ($y_{2i}$) since the teacher graduated from their certification program.

Like with the prior question, I don't think this is a time series problem, but upon re-reading the prior answer, I don't think this is a panel data or longitudinal data problem either. We run, however, into similar problems to the ones I pointed out in the prior question:

  • We don't have an equal number of teachers in each year for which teachers graduate.
  • If my sample is insufficient so that some calendar years were skipped, I will have data for some calendar years but not for others, breaking the usual "equal-spacing" assumption with time series.
  • The data are probably not stationary if we were to consider using the graduation year as an index for time.
  • We could attempt to bin graduation years together, but such a mechanism has no precedent (i.e., assume no similar study has been done), and would be quite arbitrary to implement.
  • Given $t_i$, we also suspect that $\sum_{\{i : u_i \text{ graduated in year }t_i\}}\dfrac{y_{1i}}{y_{1i} + y_{2i}}$ (the rate at which As were given) would be similar for values of $t_i$ that are close to each other, so any binning of graduation years we do would ignore this to an extent that I would not be comfortable with without adequate justification.

Additionally, there's an aspect of this that should be controlled for: teachers who have graduated at an earlier year naturally have higher counts in $\mathbf{y}_i$ than those who graduated at a later year.

I suspect this is more complex than viewing this as a time series or longitudinal data problem. What technique(s) would you suggest for approaching this problem?