The 2023 Huashu Cup is a competition with the same frequency as the national competition (the questions are issued at 6:00 on Thursday and the papers are handed in at 8:00 on Sunday), and it is also the only official competition in the summer. This year's registration team has reached more than 6,000 pairs. Based on such a large number of people for team practice before the national competition, and other purposes. In order to make it easier for everyone to choose a better topic, here we first analyze the ideas of Question C of the Huashu Cup. The number of questions is relatively large, but the difficulty of the questions is the lowest in this competition. Therefore, the corresponding number of selected topics may also be the largest one. Therefore, how to stand out from the crowd requires attention to many details, which will be explained later in the explanation of ideas.
Question C: The influence of the mother’s physical and mental health on the growth of the baby
The questions were drawn based on the background of mother-related indicators and infant sleep. A data set is given, including data on 390 infants aged 3 to 12 months and their mothers. The data cover a variety of subjects, with physical indicators of mothers including age, marital status, education, duration of pregnancy, mode of delivery, and maternal psychological indicators CBTS (Partnership-related Post Traumatic Stress Disorder Questionnaire), EPDS (Edinburgh Postpartum Depression Scale) , HADS (Hospital Anxiety and Depression Scale) and indicators of infant sleep quality including duration of sleep throughout the night, number of awakenings and falling asleep patterns.
For data type questions, the first step is not to directly read the question, but to process the data. There must be outliers and missing values for the following data sets. Therefore, data preprocessing is necessary first.
For example, for data such as marital status. Marital status, unmarried and married, but there are people whose marital status is 3 and 6 are outliers. Such data needs to be processed. As for the processing method, choose elimination or interpolation processing, etc., just choose according to the team situation.
1. Many studies have shown that the mother's physical and psychological indicators have an impact on the baby's behavioral characteristics and sleep quality. Is there such a rule? Do research based on the data in the attachment.
Question 1, whether there is such a law, that is, to conduct simple analysis results, draw a scatter diagram, and perform correlation analysis; for correlation analysis, you can choose Pearson'Pearson'correlation coefficient, Spearman'Spearman'correlation Coefficient or other correlation coefficient indicators, it is enough to express that there is such a law. Remember that the question is only asked, is there such a law? Existence is not necessary to derive specific relational expressions. Don’t overdo it. The first innovation point of the problem is the scatter plot. You can draw it better, and pay attention to the visual expression of the results.
2. The Infant Behavior Questionnaire is a scale used to assess behavioral characteristics of infants, which contains a number of questions about the infant's emotions and reactions. We divide the behavioral characteristics of infants into three types: quiet, moderate, and ambivalent. Please establish a relationship model between the baby's behavioral characteristics and the mother's physical and psychological indicators. In the last 20 groups of infants (No. 391-410) in the data table, the behavior characteristics information has been deleted. Please judge what type they belong to.
Question 2, the infant behavior questionnaire and scale questions need to be tested for reliability and validity of the questionnaire. For the specific steps, you can refer to the 32 CP Cup excellent papers I gave. The necessary reliability and validity tests are carried out in the same way as the excellent papers in questionnaire competitions.
Question 2 requires us to establish a relationship model between the baby’s behavioral characteristics and the mother’s physical and psychological indicators, that is, to establish a relationship model between one y and multiple Xs. The simplest way is to directly establish a multiple regression analysis model. Although this method Simple but can correspond to the regression analysis model of question 4, the whole paper is a system. You can also choose some other more complex models.
3. Intervention on mothers' anxiety can help improve mothers' mental health, improve the quality of mother-infant interaction, and promote infants' cognitive, emotional and social development. The change rate of the treatment cost of CBTS, EPDS, and HADS relative to the degree of illness is proportional to the treatment cost. After investigation, the treatment costs corresponding to the two scores are given, as shown in Table 1. There is an infant whose behavioral characteristics are ambivalent, numbered 238. Please build a model to analyze how much treatment cost is required to change the baby's behavioral characteristics from contradictory to moderate? How would the treatment plan need to be adjusted in order to change his behavioral profile to a quieter type?
The third question is to analyze the minimum cost of treatment. The solution of the most value problem is the optimization model, and the optimization model seeks the three requirements of the optimization model, the decision variable objective function constraints. For problem three, construct an optimization model with the minimum cost as the objective function, and translate the corresponding constraints according to the title to solve it; the choice of constraints here can be: the rate of change of the treatment cost relative to the degree of illness is equal to the treatment cost is directly proportional, equality constraints can be constructed, etc.
The code package of the optimized model is also prepared for you, so that you can write the corresponding optimized code.
4. The baby's sleep quality indicators include the sleep time of the whole night, the number of times of waking up, and the way of falling asleep. Please make a comprehensive evaluation of the baby's sleep quality in four categories: excellent, good, medium, and poor, and establish a correlation model between the baby's comprehensive sleep quality and the mother's physical and psychological indicators, and predict the last 20 groups (No. 391-410) Overall sleep quality in infants.
Question 4 is divided into two parts: 1. Comprehensive evaluation; 2. Predict the last 20 sets of data. For the evaluation model of question 4, you can choose the appropriate model yourself, and try to choose an objective evaluation model. Here, what needs to be considered is that the final results need to be comprehensively judged in four categories: excellent, good, medium, and poor. Therefore, the threshold value division process can be performed according to the comprehensive evaluation score obtained from the final evaluation model establishment. For example, the top 25% of the rankings are considered excellent; 25%-50% are considered good.
For the second half of the forecast, it belongs to multiple independent variables and multiple dependent variables. Therefore, my personal opinion here is to recommend that you use partial least squares regression analysis. As for everyone who has a better idea, you can also try it.
5. On the basis of Question 3, if it is necessary to make the sleep quality of baby No. 238 rated as excellent, does the treatment strategy for Question 3 need to be adjusted? How to adjust?
Question 5 can be solved together with Question 3, that is, Question 5 is an extension of Question 3, and a new constraint of sleep quality rating is introduced to solve it.
Summary:
Data preprocessing outliers, missing values
Question 1. Correlation Analysis Multivariate Analysis (Partial Least Squares)
Question 2: Reliability and Validity Analysis of the Questionnaire Multiple Regression Analysis (Partial Least Squares) Using the Model to Predict
Question 3: Optimizing the Model
Question 4.1. Comprehensive evaluation + comprehensive value threshold setting
2. Partial least squares regression analysis
Question 5. Introduction of New Constraints Expansion of Question 3
Estimated number of topic candidates: A:B:C=1:2:4
In the future, due to limited personal energy, this competition will choose question C as the writing topic of semi-finished papers and complete papers. These two papers will also be displayed on August 4th to provide you with a reference answer, which is convenient for everyone to better do the questions.