Within statistics, Local independence is the underlying assumption of latent variable models (such as factor analysis and item response theory models).The observed items are conditionally independent of each other given an individual score on the latent variable(s). This means that the latent variable(s) in a model fully explain why the observed items are related to one another. This can be explained by the following example.
Local independence can be explained by an example of Lazarsfeld and Henry (1968). Suppose that a sample of 1000 people was asked whether they read journals A and B. Their responses were as follows:
| Read A | Did not read A | Total | ||
| Read B | 260 | 140 | 400 | |
| Did not read B | 240 | 360 | 600 | |
| Total | 500 | 500 | 1000 |
One can easily see that the two variables (reading A and reading B) are strongly related, and thus dependent on each other. Readers of A tend to read B more often (52%=260/500) than non-readers of A (28%=140/500). If reading A and B were independent, then the formula P(A&B) = P(A)×P(B) would hold. But 260/1000 isn't 400/1000 × 500/1000. Thus, reading A and B are statistically dependent on each other.
If the analysis is extended to also look at the education level of these people, the following tables are found.
| High education | Read A | Did not read A | Total | |
| Read B | 240 | 60 | 300 | |
| Did not read B | 160 | 40 | 200 | |
| Total | 400 | 100 | 500 |
| Low education | Read A | Did not read A | Total | |
| Read B | 20 | 80 | 100 | |
| Did not read B | 80 | 320 | 400 | |
| Total | 100 | 400 | 500 |