The location model proposed in the past is a predictive discriminant rule that can classify new observations into one
of two predefined groups based on mixtures of continuous and categorical variables. The ability of location model to
discriminate new observation correctly is highly dependent on the number of multinomial cells created by the number
of categorical variables. This study conducts a preliminary investigation to show the location model that uses maximum
likelihood estimation has high misclassification rate up to 45% on average in dealing with more than six categorical
variables for all 36 data tested. Such model indicated highly incorrect prediction as this model performed badly for
large categorical variables even with large sample size. To alleviate the high rate of misclassification, a new strategy
is embedded in the discriminant rule by introducing nonlinear principal component analysis (NPCA) into the classical
location model (cLM), mainly to handle the large number of categorical variables. This new strategy is investigated
on some simulation and real datasets through the estimation of misclassification rate using leave-one-out method. The
results from numerical investigations manifest the feasibility of the proposed model as the misclassification rate is
dramatically decreased compared to the cLM for all 18 different data settings. A practical application using real dataset
demonstrates a significant improvement and obtains comparable result among the best methods that are compared. The
overall findings reveal that the proposed model extended the applicability range of the location model as previously it
was limited to only six categorical variables to achieve acceptable performance. This study proved that the proposed
model with new discrimination procedure can be used as an alternative to the problems of mixed variables classification,
primarily when facing with large categorical variables.
This article investigates the performance of two-sample pseudo-median based procedure in testing differences between groups. The procedure is a modification of the one-sample Wilcoxon procedure using the pseudo-median of differences between group values as the central measure of location. The test was conducted on two groups with moderate sample
sizes of symmetric and asymmetric distributions. The performance of the procedure was measured in terms of Type I error and power rates computed via Monte Carlo methods. The performance of the procedure was compared against the t-test and Mann-Whitney-Wilcoxon test. The findings from this study revealed that the pseudo-median procedure performed very
well in controlling Type I error rates close to the nominal value. The pseudo-median procedure outperformed the MannWhitney-Wilcoxon test and is comparable to the t-test in controlling Type I error and maintaining adequate power.
Ujian Alexander-Govern merupakan ujian kesamaan sukatan memusat yang teguh pada keadaan varians heterogen. Malangnya ujian ini tidak teguh pada keadaan data tidak normal. Adaptasi penganggar teguh seperti penganggar M satu langkah terubah suai (MOM) sebagai sukatan memusat menggantikan min didapati berupaya meningkatkan keteguhan ujian ini apabila dijalankan pada data terpencong. Penganggar ini mempunyai kelebihan berbanding min kerana tidak dipengaruhi oleh data yang tidak normal. Kajian ini mendapati bahawa ujian Alexander-Govern yang telah diubah suai ini berupaya mengawal Ralat Jenis I dengan baik pada data terpencong untuk semua keadaan. Kadar Ralat Jenis I yang dihasilkan kebanyakannya berada di dalam selang kriteria teguh ketat (0.045 hingga 0.055) pada aras keertian 0.05. Berbeza dengan kaedah pengujian asal yang mana pada kebanyakan keadaan, ujian teguh tetapi hanya dengan kriteria liberal (0.025 hingga 0.075), malahan ada kedaan yang mana ujian tidak teguh. Prestasi kaedah yang diubah suai ini juga setanding dengan keadah asal pada keadaan data normal. Kajian ini juga membandingkan kaedah Alexander Govern yang diubah suai dengan kaedah pengujian klasik seperti ujian-t dan ANO VA dan menyaksikan bahawa kaedah klasik tidak teguh pada keadaan varians heterogen.
An alternative robust method for testing the equality of central tendency measures was developed by integrating H Statistic with adaptive trimmed mean using hinge estimator, HQ. H Statistic is known for its ability to control Type I error rates and HQ is a robust location estimator. This robust estimator used asymmetric trimming technique, where it trims the tail of the distribution based on the characteristic of that particular distribution. To investigate on the performance (i.e. robustness) of the procedure, some variables were manipulated to create conditions which are known to highlight its strengths and weaknesses. Bootstrap method was used to test the hypothesis. The integration seemed to produce promising robust procedure that is capable of addressing the problem of violations to the assumptions. About 20% trimming is the appropriate amount of trimming for the procedure, where this amount is found to be robust in most conditions. This procedure was also proven to be robust as compared to the parametric (AN0vA) and non parametric (Kruskal-Wallis) methods.