. 2023 Jul 10;120(29):e2304862120. doi: 10.1073/pnas.2304862120

Table 1.

Model results

	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6	Model 7	Model 8	Model 9	Model 10
Fixed effects	$\hat{β}$	$\hat{β}$	$\hat{β}$	$\hat{β}$	$\hat{β}$	$\hat{β}$	$\hat{β}$	$\hat{β}$	$\hat{β}$	$\hat{β}$
(Intercept)	1.515***	1.467***	1.466***	1.464***	1.462***	1.458***	1.513***	−1.382***	1.486***	1.841***
YSP	0.972***	0.991***	1.006***	1.019***	1.022***	1.018***	0.744***	0.971***	1.03***	1.065***
YSP²	−0.251***	−0.257***	−0.266***	−0.273***	−0.275***	−0.272***	−0.13***	−0.252***	−0.287***	−0.267***
YSP³	0.033***	0.034***	0.036***	0.038***	0.038***	0.038***	0.011***	0.033***	0.042***	0.035***
YSP⁴	−0.002***	−0.002***	0.002***	−0.002***	−0.003***	−0.002***	−0.0004***	−0.002***	−0.003***	−0.002***
YSP⁵	0.0001***	0.0001***	0.0001***	0.0001***	0.0001***	0.0001***	0.00001***	0.0001***	0.0001***	0.0001***
Published		0.04***	0.04***	0.034**	0.032**	0.032***	0.03**	0.032***	0.035***	0.062***
YSP × Published		−0.004***	0.004***	−0.001**	−0.001	−0.001**	−0.0003	−0.004***	−0.0005	−0.003***
FRP			−0.167***	−0.146***	−0.137***	−0.148***	−0.137***	0.01	−0.27**	−0.057**
YS_FRP				−0.094***	−0.122***	−0.095***	−0.091***	−0.045***	−0.113**	−0.066***
Replicated					0.011
YSP × Replicated					−0.002
Published × Replicated					0.002
YS_FRP × Replicated					−0.008*
Random effects	SD	SD	SD	SD	SD	SD	SD	SD
Paper	1.055	1.056	1.05	1.042	1.044	1.039	1.066	0
Residual	0.462	0.446	0.444	0.434	0.434	0.434	0.451	0.427

Notes: *** = P < 0.001, ** = P < 0.01, and * = P < 0.05. YSP = years since publication, Published = year of publication (mean-centered), FRP = failed replication (0 = no, 1 = yes), YS_FRP = years since failed replication, Replicated = year of replication (mean-centered). Models 1 to 5 are HLMs predicting logged citation rates within the first 14 y postpublication excluding one outlying paper. Model 6 adds the outlying paper back to the dataset. Model 7 extends the time window of data used in the model to include the first 25 y postpublication (92.3% of all data). Model 8 predicts logged citations mean-centered within papers. Model 9 is a linear model using heteroskedasticity- and cluster-robust SEs. Model 10 is a generalized estimating equation model predicting raw citation counts using a Poisson error distribution and an autoregressive correlation structure (AR-M) correlation structure. Bold indicates the variables of primary interest.