Question

As mentioned in Topic#1 for this week, the issues of validity and reliability are critical when evaluating your regression model. For reliability the most significant issues are serial correlation, heteroscedasticity and collinearity. What are these issues and how do they affect the reliability of our regression model? And how can we spot them if they are there?

Answer 1

There are various concepts which are utilized to evaluate the quality of research. They indicate the efficiency of the technique as they test each measures. The issues of validity and reliability are critical during evaluation of regression model. Reliability is about the consistency of a measure, and validity is about the accuracy of a measure. However, few issues have been found with the use of reliability as a metric.

The most significant issues for reliability are below:

1. Serial correlation -

When error terms from different (usually adjacent) time periods (or cross-section observations) are correlated, we say that the error term is serially correlated. Serial correlation occurs in time-series studies when the errors associated with a given time period carry over into future time periods.

Issue -

Serial correlation will not affect the unbiasedness or consistency of estimators, but it does affect their efficiency. With positive serial correlation, the estimates of the standard errors will be smaller than the true standard errors. This will lead to the conclusion that the parameter estimates are more precise than they really are. There will be a tendency to reject the null hypothesis when it should not be rejected.

To identify the issue -

The presence of serial correlation can be detected by the Durbin-Watson test and by plotting the residuals against their lags. The subscript t represents the time period. In econometric work, these u's are often called the disturbances. They are the ultimate error terms.

2. Heteroscedasticity :

Heteroscedasticity refers to unequal scatter. Heteroscedasticity is a systematic change in the spread of the residuals over the range of measured values.

Issue -

Heteroscedasticity is a problem because ordinary least squares (OLS) regression assumes that all residuals are drawn from a population that has a constant variance (homoscedasticity).

To identify the issue -

This method produces a distinctive fan or cone shape in residual plots. To check for heteroscedasticity, you need to assess the residuals by fitted value plots specifically. Typically, the telltale pattern for heteroscedasticity is that as the fitted values increases, the variance of the residuals also increases. If there are patterns in the models, the model has a problem.

3. Collinearity

Multicollinearity occurs when independent variables in a regression model are correlated.

Issue -

This correlation is a problem because independent variables should be independent. If the degree of correlation between variables is high enough, it can cause problems when you fit the model and interpret the results.

To identify the issue-

Examine the correlation coefficient for each pair of independent variables. A value of the correlation near ±1 indicates that the two variables are highly correlated. Use Analyze → Correlate → Bivariate in SPSS to obtain the correlation coefficients.