www.gusucode.com > stats 源码程序 matlab案例代码 > stats/FTestsforFixedEffectsExample.m
%% F-Tests for Fixed Effects %% % Load the sample data. load(fullfile(matlabroot,'examples','stats','shift.mat')) %% % The data shows the deviations from the target quality characteristic measured % from the products that five operators manufacture during three shifts: % morning, evening, and night. This is a randomized block design, where % the operators are the blocks. The experiment is designed to study the % impact of the time of shift on the performance. The performance measure % is the deviation of the quality characteristics from the target value. % This is simulated data. %% % |Shift| and |Operator| are nominal variables. shift.Shift = nominal(shift.Shift); shift.Operator = nominal(shift.Operator); %% % Fit a linear mixed-effects model with a random intercept grouped by operator % to assess if performance significantly differs according to the time of % the shift. Use the restricted maximum likelihood method and |'effects'| % contrasts. % % |'effects'| contrasts indicate that the coefficients sum to 0, and |fitlme| % creates two contrast-coded variables in the fixed-effects design matrix, % $X$1 and $X$2, where % % $$Shift{\rm{\_}}Evening = \left\{ {\begin{array}{*{20}{c}} % {0,\quad if\;Morning}\\ % {1,\quad if\;Evening}\\ % { -1,\quad if\;Night} % \end{array}}\right.$$ % % and % % $$Shift{\rm{\_}}Morning = \left\{ {\begin{array}{*{20}{c}} % {1,\quad if\;Morning}\\ % {0,\quad if\;Evening}\\ % { - 1,\quad if\;Night } % \end{array}}\right..$$ % % The model corresponds to % % $$\begin{array}{l} % {\rm{Morning Shift: }}QCDe{v_{im}} = {\beta _0} + {\beta _2}Shift{\rm{\_}}Mornin{g_i} + {b_{0m}} + {\varepsilon _{im}},\quad m = 1,2,...,5,\\ % {\rm{Evening Shift: }}QCDe{v_{im}} = {\beta _0} + {\beta _1}Shift{\rm{\_}}Evenin{g_i} + {b_{0m}} + {\varepsilon _{im}},\\ % {\rm{Night Shift: }}\quad QCDe{v_{im}} = {\beta _0} - {\beta _1}Shift{\rm{\_}}Evenin{g_i} - {\beta _2}Shift{\rm{\_}}Mornin{g_i} + {b_{0m}} + {\varepsilon _{im}}, % \end{array}$$ % % where $b$ ~ N(0, $\sigma^{2}_{b}$ ) and $\epsilon$ % ~ N(0, $\sigma^{2}$ ). lme = fitlme(shift,'QCDev ~ Shift + (1|Operator)',... 'FitMethod','REML','DummyVarCoding','effects') %% % Perform an $F$-test to determine if all fixed-effects coefficients are 0. anova(lme) %% % The $p$-value for the constant term, 0.0021832, is the same as in the % coefficient table in the |lme| display. The $p$-value of 0.0018721 for % |Shift| measures the combined significance for both coefficients representing % |Shift|.