Calculation of pathway values, defined as the difference between residuals of full model and reduced model lacking the pathway variable. The larger the difference, the more a case qualifies as a pathway case suitable for the analysis of mechanisms.
pathway(full_model, reduced_model)
| full_model | Full model including covariate of interest (= pathway variable) |
|---|---|
| reduced_model | Reduced model excluding covariate of interest |
A dataframe with
- all full model variables,
- full model residuals (full_resid),
- reduced model residuals (reduced_resid),
- pathway values following Weller/Barnes (pathway_wb),
- pathway values following Gerring (pathway_gvalue),
- variable showing whether Gerring's criterion for a pathway
case is met (pathway_gstatus)
The difference between the absolute residuals of the full and reduced model follows the approach developed by Weller and Barnes (2014): Finding Pathways: Mixed-Method Research for Studying Causal Mechanisms. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9781139644501).
The calculation of the absolute difference between the full-model and reduced-model residuals, given a case's reduced-model residual is larger than its full-model residual, follows the proposal by Gerring (2007): Is There a (Viable) Crucial-Case Method? Comparative Political Studies 40 (3): 231-253. https://journals.sagepub.com/doi/10.1177/0010414006290784)
df_full <- lm(mpg ~ disp + wt, data = mtcars) df_reduced <- lm(mpg ~ wt, data = mtcars) pathway(df_full, df_reduced)#> mpg disp wt full_resid reduced_resid pathway_wb #> Mazda RX4 21.0 160.0 2.620 -2.34543258 -2.2826106 -0.06282193 #> Mazda RX4 Wag 21.0 160.0 2.875 -1.49097212 -0.9197704 -0.57120172 #> Datsun 710 22.8 108.0 2.320 -2.47236688 -2.0859521 -0.38641476 #> Hornet 4 Drive 21.4 258.0 3.215 1.78533343 1.2973499 -0.48798349 #> Hornet Sportabout 18.7 360.0 3.440 1.64719305 -0.2001440 -1.44704909 #> Valiant 18.1 225.0 3.460 -1.27863092 -0.6932545 -0.58537640 #> Duster 360 14.3 360.0 3.570 -2.31719966 -3.9053627 1.58816299 #> Merc 240D 24.4 146.7 3.190 2.72879876 4.1637381 1.43493939 #> Merc 230 22.8 140.8 3.150 0.89018976 2.3499593 1.45976953 #> Merc 280 19.2 167.6 3.440 -1.26304775 0.2998560 -0.96319171 #> Merc 280C 17.8 167.6 3.440 -2.66304775 -1.1001440 -1.56290379 #> Merc 450SE 16.4 275.8 4.070 -0.03421046 0.8668731 0.83266267 #> Merc 450SL 17.3 275.8 3.730 -0.27349107 -0.0502472 -0.22324387 #> Merc 450SLC 15.2 275.8 3.780 -2.20594981 -1.8830236 -0.32292618 #> Cadillac Fleetwood 10.4 472.0 5.250 1.39735826 1.1733496 -0.22400867 #> Lincoln Continental 10.4 460.0 5.424 1.76770494 2.1032876 0.33558271 #> Chrysler Imperial 14.7 440.0 5.345 5.44849485 5.9810744 0.53257954 #> Fiat 128 32.4 78.7 2.200 6.20619907 6.8727113 0.66651222 #> Honda Civic 30.4 75.7 1.615 2.19279202 1.7461954 -0.44659660 #> Toyota Corolla 33.9 71.1 1.835 6.34843977 6.4219792 0.07353940 #> Toyota Corona 21.5 120.1 2.465 -3.07202780 -2.6110037 -0.46102406 #> Dodge Challenger 15.5 318.0 3.520 -2.02918018 -2.9725862 0.94340605 #> AMC Javelin 15.2 304.0 3.435 -2.86214676 -3.7268663 0.86471956 #> Camaro Z28 13.3 350.0 3.840 -2.58972426 -3.4623553 0.87263107 #> Pontiac Firebird 19.2 400.0 3.845 4.21326708 2.4643670 -1.74890005 #> Fiat X1-9 27.3 79.0 1.935 0.22354778 0.3564263 0.13287854 #> Porsche 914-2 26.0 120.3 2.140 0.34249891 0.1520430 -0.19045591 #> Lotus Europa 30.4 95.1 1.513 2.19486787 1.2010593 -0.99380855 #> Ford Pantera L 15.8 351.0 3.170 -2.31705249 -4.5431513 2.22609879 #> Ferrari Dino 19.7 145.0 2.770 -3.40867994 -2.7809399 -0.62774003 #> Maserati Bora 15.0 301.0 3.570 -2.66295957 -3.2053627 0.54240308 #> Volvo 142E 21.4 121.0 2.780 -2.10056555 -1.0274952 -1.07307036 #> pathway_gvalue pathway_gtype #> Mazda RX4 0.06282193 no #> Mazda RX4 Wag 0.57120172 no #> Datsun 710 0.38641476 no #> Hornet 4 Drive 0.48798349 no #> Hornet Sportabout 1.84733701 no #> Valiant 0.58537640 no #> Duster 360 1.58816299 yes #> Merc 240D 1.43493939 yes #> Merc 230 1.45976953 yes #> Merc 280 1.56290379 no #> Merc 280C 1.56290379 no #> Merc 450SE 0.90108359 yes #> Merc 450SL 0.22324387 no #> Merc 450SLC 0.32292618 no #> Cadillac Fleetwood 0.22400867 no #> Lincoln Continental 0.33558271 yes #> Chrysler Imperial 0.53257954 yes #> Fiat 128 0.66651222 yes #> Honda Civic 0.44659660 no #> Toyota Corolla 0.07353940 yes #> Toyota Corona 0.46102406 no #> Dodge Challenger 0.94340605 yes #> AMC Javelin 0.86471956 yes #> Camaro Z28 0.87263107 yes #> Pontiac Firebird 1.74890005 no #> Fiat X1-9 0.13287854 yes #> Porsche 914-2 0.19045591 no #> Lotus Europa 0.99380855 no #> Ford Pantera L 2.22609879 yes #> Ferrari Dino 0.62774003 no #> Maserati Bora 0.54240308 yes #> Volvo 142E 1.07307036 no