#### True DGP:

#### Estimated Model:

#### Simulation Results

Set values at left, click 'Simulate!' button to run, and wait 3-15 seconds for results to appear (see loading bar at lower right).

#### Why does right-censored data matter?

Censoring is one of the most frequently mentioned reasons for OLS' inappropriateness. A (right-)censored duration is one where a subject does not fail before our observation period ends. As a result, we do not observe their actual failure time. Instead, we only know they survived *up to* the end of our observation period. Right censoring creates a problem for OLS because the estimator cannot handle it. Instead, OLS treats all subjects as failing at the time we record, which is clearly not true.

#### What should I see?

From the 'Non-Normal' tab, we've already established that OLS with the untransformed duration performs poorly because of non-linearity in parameters. Right-censored data makes OLS' performance even worse, because OLS' inability to model right censoring properly. As a consequence, the estimates will be

*biased*
and

*inefficient.*
#### Where should I look to see that?

**Biased:**
Top two rows won't match for all columns; top row won't fall in between values in 3rd and 4th rows for all columns. Additionally, these estimates will also differ from the OLS estimates on the 'Non-Normal' tab (provided that all common slider/field values are identical).

**Inefficient:**
5th row's values will be larger than the Weibull's 5th row (for a very rough heuristic; the Weibull constitutes the 'No Violations' scenario).

#### Why does right-censored data matter?

Censoring is one of the most frequently mentioned reasons for OLS' inappropriateness. A (right-)censored duration is one where a subject does not fail before our observation period ends. As a result, we do not observe their actual failure time. Instead, we only know they survived *up to* the end of our observation period. Right censoring creates a problem for OLS because the estimator cannot handle it. Instead, OLS treats all subjects as failing at the time we record, which is clearly not true.

#### What should I see?

Despite our transformation of

*t*
to remove the non-linearity in parameters, these OLS estimates will still be

*biased*
and

*inefficient,*
because OLS's inability to properly model right-censored durations.

#### Where should I look to see that?

**Biased:**
Top two rows won't match for all columns; top row won't fall in between values in 3rd and 4th rows for all columns.

**Inefficient:**
5th row's values will be larger than the Weibull's 5th row (for a very rough heuristic; the Weibull constitutes the 'No Violations' scenario).

#### Why does right-censored data matter?

Censoring is one of the most frequently mentioned reasons for OLS' inappropriateness. A (right-)censored duration is one where a subject does not fail before our observation period ends. As a result, we do not observe their actual failure time. Instead, we only know they survived *up to* the end of our observation period. Right censoring creates a problem for OLS because the estimator cannot handle it. Instead, OLS treats all subjects as failing at the time we record, which is clearly not true.

#### What should I see?

Censored linear regression is a special type of linear regression that can handle right censoring. Therefore, the estimates will now be

*unbiased*
except for the constant term, which will still be biased because OLS does not *explicitly* model the shape parameter. However, censored linear regression assumes the errors are normally distributed, same as OLS (which is potentially problematic, see 'Non-Normal Errors' tab). As a result, the standard errors will still be

*inefficient.*
#### Where should I look to see that?

**Unbiased:**
Top two rows should match/be close for all columns except intercept and shape; top row should fall in between values in 3rd and 4th rows for all columns.

**Inefficient:**
5th row's values will be larger than the Weibull's 5th row (for a very rough heuristic; the Weibull constitutes the 'No Violations' scenario).

#### Why does right-censored data matter?

Censoring is one of the most frequently mentioned reasons for OLS' inappropriateness. A (right-)censored duration is one where a subject does not fail before our observation period ends. As a result, we do not observe their actual failure time. Instead, we only know they survived *up to* the end of our observation period. Right censoring creates a problem for OLS because the estimator cannot handle it. Instead, OLS treats all subjects as failing at the time we record, which is clearly not true.

#### What should I see?

We already know the Weibull duration model assumes non-normal errors (TIEVmin, specifically; see 'Non-Normal Errors' tab). In addition, though, all duration models can handle right-censored data by modeling it properly (i.e., not treating the censored observations as if they are observed failure times). The Weibull is no exception. As a result, the Weibull estimates will be both

*unbiased*
and

*efficient.*
#### Where should I look to see that?

**Unbiased:**
Top two rows should match/be close for all columns; top row should fall in between values in 3rd and 4th rows for all columns.

**Efficient:**
5th row will be smallest of all three models' fifth rows (for a very rough heuristic). Additionally, 5th and 6th rows will match/be close for all columns.