Hierarchical regression (blocks)

In brief

The columns under "Predicted from what?" are tested in 2 or 3 blocks. Each block shows how much variance it explains beyond the previous blocks (ΔR²).

What for

Typical: block 1 holds control variables (for example age), block 2 the variable of interest. "Build blocks" is chosen under "More options" in the question "Can something be predicted?". Without blocks the regression stays as usual.

Requirements

• As for linear regression. If the target column has exactly two values, Statable calculates without blocks.
• The order of the blocks is fixed before the analysis and justified by theory, not chosen after seeing the result.
• All blocks are calculated on the same cases: anyone with a gap in a later block is also missing from block 1. Statable states the number of these cases.

Reading the result

• Per block R², adjusted R², ΔR² and the F change with df1 (new coefficients; a group column with k levels counts k − 1), df2 and p. Block 1 is tested against a model without predictors.
• Significant ΔR²: the block explains further variance beyond the previous ones. Otherwise: no significant share. If the adjusted R² falls, the block adds nothing after the chance gain is deducted.
• The coefficients (B, β, p) belong to the model with all blocks.

Reporting the result

Block 1: R² = .10, F(2, 97) = 5.53, p = .005; Block 2: ΔR² = .23, F(2, 95) = 16.06, p < .001

In the text, name the columns of each block and justify the order.

Limits

• ΔR² is not proof of causation: it shows how much variance a block explains in addition, not that it causes it.
• A different order gives different ΔR². PSPP calculates one model per block; Statable calculates ΔR² and the F change (as SPSS "F Change", in R pairwise anova(m1, m2)).

Source

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (3rd ed.). Erlbaum. Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.), ch. 9. Sage.