Nurses' experiences and preferences around shift patterns: A scoping review

Structural change detection in ordinal time series

make accurate predictions removedgraphic cumulative logistic regression
structural change of cumulative logistic regression

yes">j=1, 2...,<italic toggle="yes">m,<italic toggle="yes">t=1, 2
toggle="yes">t -1 +<italic toggle="yes">e<italic toggle="yes">t,<italic toggle="yes">b ∈<italic toggle="yes">R^<italic toggle="yes">d,<italic toggle="yes">z<italic toggle="yes">t -1
toggle="yes">x /(1 -<italic toggle="yes">x), 0<<italic toggle="yes">x<1
we have<disp formula id="pone.0256128.e009">removedGRAPHIC log i t(P Y t<=j | F t -1)=alpha j + b ' z t -1, j=1, 2
Thepartiallikelihood function<disp formula id="pone.0256128.e013">removedGRAPHIC P L (θ)=∏ t=1
likelihood function<disp formula id="pone.0256128.e014">removedGRAPHIC l (θ)=log P L (θ)=∑ t=1 n ∑ j=1
thepartialscore vector<disp formula id="pone.0256128.e015">removedGRAPHIC S n (θ)=∇ l (θ)=(∂ l (θ) ∂ θ 1..., ∂ l (θ) ∂ θ p) '=∑ t=1
yes">h 1 (<italic toggle="yes">eta<italic toggle="yes">t)...,<italic toggle="yes">h<italic toggle="yes">q (<italic toggle="yes">eta<italic toggle="yes">t) satisfies<disp formula id="pone.0256128.e020">removedGRAPHIC π t 1 (θ)=h 1 eta t 1)=F eta t 1)..., π t j (θ)=h j eta t=F eta t j - F eta t(j -1), j=2
toggle="yes">t) !=0,<italic toggle="yes">where removedGRAPHIC eta t=Z t -1 ' θ. Assumption 3<italic toggle="yes">The covariate matrix<italic toggle="yes">Z<italic toggle="yes">t -1
From Assumption 3,<disp formula id="pone.0256128.e029">removedGRAPHIC G n (θ)=∑ t=1
have Assumption 6 removedGRAPHIC E | z t -1 i | 4<∞,<italic toggle="yes">i=1, 2, ⋯,<italic toggle="yes">d,<italic toggle="yes">where removedGRAPHIC z t -1 i, 1
H 0<italic toggle="yes">hold, then we have<disp formula id="pone.0256128.e052">removedGRAPHIC W 1=max 1<=k<=n n -1 / 2 T^n -1 / 2 S k (θ^n) ->d sup 0<t<1 B t,</disp formula><italic toggle="yes">where removedGRAPHIC T^n=1
S n (θ^n)=0, we can write<disp formula id="pone.0256128.e056">removedGRAPHIC n -1 / 2 S k (θ^n)=n -1 / 2
toggle="yes">i=1, 2...,<italic toggle="yes">p,<italic toggle="yes">θ 0
pone.0256128.e059">removedGRAPHIC max 1<=k<=n 1 n | ∑ t=1
we get<disp formula id="pone.0256128.e064">removedGRAPHIC max 1<=k<=n n -1 / 2 T^n -1 / 2 S k (θ^n) ->d sup 0<t<1
where<disp formula id="pone.0256128.e068">removedGRAPHIC ξ k=(T^n -1 / 2 S k (θ^n) (i 1)..., (T^n -1 / 2 S k (θ^n) i j ',</disp formula>{<italic toggle="yes">i 1,<italic toggle="yes">i 2 ...,<italic toggle="yes">i<italic toggle="yes">j } ⊂ {1, 2...,<italic toggle="yes">p },<italic toggle="yes">j=1, 2...,<italic toggle="yes">p, 0<<italic toggle="yes">l<<italic toggle="yes">h<1
H 0<italic toggle="yes">hold, then we have<disp formula id="pone.0256128.e069">removedGRAPHIC W 2=max l<k n<h n -1 ξ k ' ξ k k / n (1 - k / n) ->d sup l<t<h ∑ i=1
t(1 - t)</disp formula><italic toggle="yes">for each 0<<italic toggle="yes">l<<italic toggle="yes">h<1,<italic toggle="yes">B<italic toggle="yes">i (<italic toggle="yes">t),<italic toggle="yes">i=1
pone.0256128.e070">removedGRAPHIC P { sup l<t<h ∑ i=1
yes">delta !=0,<italic toggle="yes">then we have -<disp formula id="pone.0256128.e074">removedGRAPHIC W 1=max 1<=k<=n n -1 / 2 ‖ T^n -1 / 2 S k (θ^n) ‖ ->P ∞ ;</disp formula>-<disp formula id="pone.0256128.e075">removedGRAPHIC W 2=max l<k n<h n -1 ξ k ' ξ k k / n (1 - k / n) ->P ∞,</disp formula><p specific use="continuation">where 0<<italic toggle="yes">l<<italic toggle="yes">h<1
toggle="yes">delta>0 arbitrarily<disp formula id="pone.0256128.e109">removedGRAPHIC lim n ->∞ P { n -1 / 2
yes">alpha 1=-0.5,<italic toggle="yes">alpha 2=0.2, (<italic toggle="yes">b 1,<italic toggle="yes">b 2,<italic toggle="yes">b 3)'=(2, 0.5, 1
toggle="yes">alpha 1,<italic toggle="yes">alpha 2,<italic toggle="yes">alpha 3,<italic toggle="yes">b 1,<italic toggle="yes">b 2,<italic toggle="yes">b 3
critical is 1.35 when<italic toggle="yes">p=1,<italic toggle="yes">alpha=0.05