LitCovid-sentences  

PMC:7210464 / 90209-92260 JSONTXT 4 Projects

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Id Subject Object Predicate Lexical cue
T868 0-11 Sentence denotes Appendix C.
T869 12-42 Sentence denotes Computation of counterfactuals
T870 43-60 Sentence denotes Our main model is
T871 61-195 Sentence denotes 4 yct=∑τ=12∑k=1Kwithinαwithin,τkh¯ctkτy¯ctτ+∑τ=12∑k=1Kbetween∑r≠cαbetween,τkm¯crtkτy¯rtτ+∑τ=12∑k=1KWuhanρτkm¯c,Wuhan,tkτz¯tτ+xctβ+𝜖ct.
T872 196-311 Sentence denotes It is convenient to write it in vector form, 5 Ynt=∑s=114Hnt,s(αwithin)+Mnt,s(αbetween)Yn,t−s+∑τ=12Zntτρτ+Xntβ+𝜖nt,
T873 312-357 Sentence denotes where Ynt=y1t⋯ynt′ and 𝜖nt are n × 1 vectors.
T874 358-519 Sentence denotes Assuming that Yns = 0 if s ≤ 0, because our sample starts on January 19, and no laboratory confirmed case was reported before January 19 in cities outside Wuhan.
T875 520-579 Sentence denotes Xnt=x1t′⋯xnt′′ is an n × k matrix of the control variables.
T876 580-716 Sentence denotes Hnt,s(αwithin) is an n × n diagonal matrix corresponding to the s-day time lag, with parameters αwithin={αwithin,τk}k=1,⋯,Kwithin,τ=1,2.
T877 717-928 Sentence denotes For example, for s = 1,⋯ , 7, the i th diagonal element of Hnt,s(αwithin) is 17∑k=1Kwithinαwithin,1kh¯ct,ik1, and for s = 8,⋯ , 14, the i th diagonal element of Hnt,s(αwithin) is 17∑k=1Kwithinαwithin,2kh¯ct,ik2.
T878 929-970 Sentence denotes Mnt,s(αbetween) is constructed similarly.
T879 971-1082 Sentence denotes For example, for s = 1,⋯ , 7 and i≠j, the ij th element of Mnt,s(αbetween) is 17∑k=1Kbetweenαbetween,1km¯ijtk1.
T880 1083-1157 Sentence denotes Zntτ is an n × KWuhan matrix corresponding to the transmission from Wuhan.
T881 1158-1218 Sentence denotes For example, the ik th element of Znt1 is m¯i,Wuhan,tk1z¯t1.
T882 1219-1306 Sentence denotes We first estimate the parameters in Eq. 4 by 2SLS and obtain the residuals 𝜖^n1,⋯,𝜖^nT.
T883 1307-1396 Sentence denotes Let ⋅^ denote the estimated value of parameters and ⋅~ denote the counterfactual changes.
T884 1397-1639 Sentence denotes The counterfactual value of Ynt is computed recursively, Y~n1=∑τ=12Z~n1τρ^τ+Xn1β^+𝜖^n1,Y~n2=∑s=11H~n2,s(α^within)+M~n2,s(α^between)Y~n,2−s+∑τ=12Z~n2τρ^τ+Xn2β^+𝜖^n2,Y~n3=∑s=12H~n3,s(α^within)+M~n3,s(α^between)Y~n,3−s+∑τ=12Z~n3τρ^τ+Xn3β^+𝜖^n3,⋮
T885 1640-1694 Sentence denotes The counterfactual change for date t is ΔYnt=Y~nt−Ynt.
T886 1695-1765 Sentence denotes The standard error of ΔYnt is obtained from 1000 bootstrap iterations.
T887 1766-1883 Sentence denotes In each bootstrap iteration, cities are sampled with replacement and the model is estimated to obtain the parameters.
T888 1884-2051 Sentence denotes The counterfactual predictions are obtained using the above equations with the estimated parameters and the counterfactual scenario (e.g., no cities adopted lockdown).