## 统计代写|R语言代写R language代考|Model formulas

In the examples above we fitted simple models. More complex ones can be easily formulated using the same syntax. First of all, one can avoid use of operator $$and explicitly define all individual main effects and interactions using operators + and :. The syntax implemented in base R allows grouping by means of parentheses, so it is also possible to exclude some interactions by combining the use of { }^ and parentheses. The same symbols as for arithmetic operators are used for model formulas. Within a formula, symbols are interpreted according to formula syntax. When we mean an arithmetic operation that could be interpreted as being part of the model formula we need to “protect” it by means of the identity function I(). The next two examples define formulas for models with only one explanatory variable. With formulas like these, the explanatory variable will be computed on the fly when fitting the model to data. In the first case below we need to explicitly protect the addition of the two variables into their sum, because otherwise they would be interpreted as two separate explanatory variables in the model. In the second case, \log () cannot be interpreted as part of the model formula, and consequently does not require additional protection, neither does the expression passed as its argument.$$
\begin{aligned}
&y \sim I\left(x 1+x_2\right) \
&y \sim \log \left(x 1+x_2\right)
\end{aligned}
$$R formula syntax allows alternative ways for specifying interaction terms. They allow “abbreviated” ways of entering formulas, which for complex experimental designs saves typing and can improve clarity. As seen above, operator * saves us from having to explicitly indicate all the interaction terms in a full factorial model.$$
y \sim x 1+x 2+x 3+x 1: x 2+x 1: x 3+x 2: x 3+x 1: x 2: x 3
$$Can be replaced by a concise equivalent.$$
y \sim x_1 * x_2 * x^3
$$When the model to be specified does not include all possible interaction terms, we can combine the concise notation with parentheses. ## 统计代写|R语言代写R language代考|Time series Longitudinal data consist of repeated measurements, usually done over time, on the same experimental units. Longitudinal data, when replicated on several experimental units at each time point, are called repeated measurements, while when not replicated, they are called time series. Base R provides special support for the analysis of time series data, while repeated measurements can be analyzed with nested linear models, mixed-effects models, and additive models. Time series data are data collected in such a way that there is only one observation, possibly of multiple variables, available at each point in time. This brief section introduces only the most basic aspects of time-series analysis. In most cases time steps are of uniform duration and occur regularly, which simplifies data handling and storage. R not only provides methods for the analysis and manipulation of time-series, but also a specialized class for their storage, “ts”. Regular time steps allow more compact storage-e.g., a ts object does not need to store time values for each observation but instead a combination of two of start time, step size and end time. We start by creating a time series from a numeric vector. By now, you surely guessed that you need to use a constructor called ts \mathrm{O} or a conversion constructor called as.ts \mathrm{O} and that you can look up the arguments they accept by reading the corresponding help pages. For example for a time series of monthly values we could use: my.ts <- ts (1: 10, start =2019, deltat =1 / 12) class(my.ts) ### [1] “ts” str(my.ts) ### Time-Series [1:10] from 2019 to 2020: 123345678910 We next use the data set austres with data on the number of Australian residents and included in R. # R语言代考 ## 统计代写|R语言代写R language代考|Model formulas 在上面的例子中，我们拟合了简单的模型。更复杂的可以使用相同的语法轻松制定。首先，可以避免使 用运算符 \\并使用运算符明确定义所有单独的主要效果和交互+和：。基本 R 中实现的语法允许通过 括号进行分组，因此也可以通过组合使用{{}^和括号。 模型公式使用与算术运算符相同的符号。在公式中，符号根据公式语法进行解释。当我们指的算术运算 可以被解释为模型公式的一部分时，我们需要通过恒等函数 10 来“保护“它。接下来的两个示例为只有一 个解释变量的模型定义了公式。使用这样的公式，解释变量将在将模型拟合到数据时动态计算。在下面 的第一种情况下，我们需要明确保护将两个变量添加到它们的总和中，否则它们将被解释为模型中的两 个单独的解释变量。在第二种情况下， \log () 不能被解释为模型公式的一部分，因此不需要额外的保护， 表达式也不需要作为其参数传递。$$
y \sim I\left(x 1+x_2\right) \quad y \sim \log \left(x 1+x_2\right)
$$R 公式语法允许指定交互项的替代方法。它们允许输入公式的“缩写”方式，这对于复杂的实验设计可以节 省打字并提高清晰度。如上所示，运算符 * 使我们不必在全因子模型中显式指示所有交互项。$$
y \sim x 1+x 2+x 3+x 1: x 2+x 1: x 3+x 2: x 3+x 1: x 2: x 3
$$可以用简洁的等价物代替。$$
y \sim x_1 * x_2 * x^3


## 统计代写|R语言代写R language代考|Time series

my.ts <- ts(1:10， 开始=2019, 出席=1/12)
class(my.ts)
### [1] “ts”
str(my.ts)
### Time-Series [1:10] from 2019 to 2020: 123345678910

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